QNT 501 Final EXAM 7

QNT 501 Final EXAM 7 QNT 501 Final EXAM 7 1. Solve for the unknown in the equation. 11A = 77 Divide both sides of the equation by the known factor to isolate the unknown value. 11 A 11 = 77 11 Now simplify. A= 7 Check. 11(7) = 77 77 = 77 Therefore, the solution of the equation is 7. 2. Solve for the unknown in the equation. B + 5 = 21 Subtract the known value from both sides of the equation to isolate the unknown value. B + 5 (5) = 21 (5) Now simplify. B = 16 Check. 16 + 5 = 21 21 = 21 Therefore, the solution of the equation is 16. 3. Solve for the unknown in the equation. X 53 = 27 Add the known value to both sides of the equation. X 53 + (53) = 27 + (53) Now simplify. X = 80 Check. 80 53 = 27 27 = 27 Therefore, the solution of the equation is 80. 4. Solve for the unknown in the equation. 5(X - 4) = 25 Eliminate the parentheses. 5X 20 + (20) = 25 + (20) Now simplify. 5X = 45 Divide both sides of the equation by the known factor to isolate the unknown value. 5X 5 = 45 5 Now simplify. X=9 Check the solution by substituting the answer in the original equation and verifying that a true statement result. The answer checks, so the solution of the equation is 9. 5. Many plans to save 1 14 of this salary each week . If his weekly salary is $ 434, find the amount he will save each week S= 1 1 ($31) S = $31 To check the solution, replace S with $31 and see if the sides are equal . ¿ $ 31 ¿ ? ¿ 1 ( $ 434 ) 14 ¿ $ 31 ¿ ? ¿ 1 ($ 434) 14 $31= $31 The answer checks Thus, Manny will save $31 each week. 6. Last week at a festival, a man sold 4 times as many tie dyed T- shirt as silk screened shirts. He sold 225 shirts altogether. How many tie-dyed shirts did he sell? Both the number of tie-dyed T-shirts and silk screened shirts are unknown, but choose one, silk-screened shirts, to be represented by a letter, N. Since the number of tie-dyed shirts is 4 times the number silk-screened shirts, represent the number of tie-dyed T-shirts as 4N. Tie-dyed shirts plus silk screened shirts equals total shirts. Write this information in symbols. N + 4N = 225 Solve the equation. Combine addends. N + 4N = 225 5N = 225 Divide both sides by 5. 5N 5 = 225 5 N = 45 The solution is 45, which represents the number of silk-screened shirts, check the solution by replacing N with 45. 45 + 4(45) = 225 45 + 180 = 225 225 = 225 The sides are equal. Therefore, the number of silk-screened shirts is 45 and the number of tie-dyed shirts is 180 7. A man ordered 3 times as many boxes of ballpoint pens as boxes of felt-tip pens. Ballpoint pens cost $4.14 per box, and felt-tip pens cost $3.05. If the mans order of pens totaled $77.35, how many boxes of each type of pen did he buy? 15.47 N 15.47 = 77.35 15.47 N=5 The solution is 5, which represent the number of boxes of felt tip pens. Check the solution by replacing N with 5. 3.05(5) + (4.14 * 3(5) ) = 77.35 3.05(5) + 12.42(5) = 77.35 15.25 + 62.10 = 77.35 77.35 = 77.35 The sides are equal. Therefore, the man ordered 5 boxes of felt-tip pens and 15 boxes of ballpoint pens. 8. For 28 hours of work, you are paid $208.60. How much would you receive for 36 hours? Set up an equation for the problem. The amount of money received for 28 hours of work is proportional to the amount of money received for 36 hours of work. $ 208.60 28 hour D dollars 36 hour = Solve the equation. 208.60 28 D 36 = 28 D = (208.60 * 36) Cross multiply. 28 D = 7,509.60 Multiply. Divide both sides by 28. 28D = 7,509.60 28 D 28 7,509.60 28 = D = 268.20 To check the solution, replace D with 268.20 and see if the sides are equal. 208.60 28 7.45 = 7.45 ¿ ? ¿ ¿ D 36 Divide. The solution checks . Therefore, you would receive $268.20 for 36 hours of work. 9. NA 10. Two part-time employees share one full time job. A girl works Mondays, Wednesdays, and Fridays, and a boy works Tuesdays and Thursdays. The job pays an annual salary of $28,632. What annual salary does each employee earn? Many businesses related problems that involve pairs of numbers that are proportional are direct proportions. That an increases in the number that pairs with it..Or, a decrease in one amount causes a decrease in the second amount. In the given problem, the job pays an annual salary of $28,632. Two employees work 5 days. Let s equal the amount of the girls salary. The amount of the annual salary, $2,632, per 5 days in proportional to the amount of the girls salary per 3 day.. Set up a proportion. 5 3 = $ 28,632 S Solve the proportion. Cross multiply. 5 S = 3 (28,632) = 85,896 Divide both sides by 5. 5S 5 = 85,896 5 S = 17,179.20 To determine the amount of the boys salary, subtract $17,179.20 from $28,632. $28,632 - $17,179.20 = $11,452.80 Therefore, the girls salary is $17, 79.20 and the boys salary is $11,452.80. 11. The formula Total cost = Cost + Shipping cost + Installation is used to find the total cost of a business asset. The formula can be written in symbols as T = C + S + I. Solve the formula for S, the shipping cost of the asset. To solve the formula for S, find an equivalent formula by rearranging it. Treat all the variables of the formula as numbers in equation. To isolate S on the right side, choose one of the terms, C or I, to subtract from both sides of the equation. First, subtract C from both sides of the equation and simplify. T=C+S+I TC=C+S+IC Subtract C from both sides of the equation. TC=S+I Next, subtract I from both sides of the equation and simplify. TC=S+I TC-I=C+S+II Subtract I from both sides of the equation. TCI=S Finally, interchange the sides of the equation. S=TCI Thus, Shipping cost = Total cost Cost Installation. 12. The formula, Salvage value = total cost depreciable Value, is used to set up a depreciation schedule for an asset. The formula can be written in symbols as S = C V. Solve the formula for C. To solve the formula for C, find an equivalent formula by rearranging it. Treat all the variables of the formula as numbers in an equation. To isolate C on the right side, add V to both sides of the equation. Solve for C. S=CV S+V=CV+V Add V to both sides of the equation. S+V=C Simplify. Finally, interchange the sides of the equation. C=S+V Therefore, total Cost = Salvage value + depreciable Value. 13. The formula, years of expected Life = depreciable Value Yearly depreciation is used to find yearly depreciation using the line depreciation method. The formula can be written in symbols as L = V Y . Solve the formula for V. To solve the formula for V , find an equivalent formula by rearranging it. Treat all the variable of the formula as number in an equation. To isolate V on the right side, multiply both sides of equation by Y . Solve for V. L= L (Y) = V Y V (Y ) Y LY = V multiply both sides of the equation by Y . Simplify. Finally, interchange the sides of the equation. V = LY Therefore, depreciable Value = years of expected Life * Yearly depreciation. 14. Write the decimal as a percent. 0.37 Recall that % means 1/100. Therefore 100% = 1. To write the decimal as a percent, multiply it by 100%. 0.37 = 0.37 * 100% Now multiply together the original number and the 100. Move the decimal point two places to the right. 0.37 * 100% = 037.% = 37% Thus, 0.37 as a percent is 37%. 15. Write the fraction as a percent. 35 100 To write the fraction as a percent, multiply it by 1 in the form of 35 100 = . ( 100 ) 1 Reduce and multiply. 35 100 ( 100 ) 1 = 35 100 Thus, = 35 100 ( 100 ) 1 35% as a percent is 35%. 16. Write the mixed number as a percent. 7 2 5 To write the fraction as a percent, multiply it by 1 in the form of 2 5 = 2 5 100 1 . ( 100 ) 1 Change the mixed number to an improper fraction. Multiply the whole-number part of the mixed number, 7, by the denominator, 5 , Then add the numerator of the mixed number, 2 , to product to get the numerator of the improper fraction. Finally, place this sum over the denominator of the mixed number to get the improper fraction. 2 5 ( 100 ) 1 = 7.5+ 2 100 5 1 ( ) = 37 5 ( 100 ) 1 Reduce and multiply. 37 5 ( 100 ) 1 = 37 5 ( 100 ) 1 = 740% Thus, 7 2 5 as a percent is740% 17. Use the appropriate form of the percentage formula. Find P if R = 33 1 3 % and B = 270. To find the portion use the formula P = RB, where R is the rate and B is the base. Rewrite the formula above substituting 33 P= (33 1 ) 3 1 3 % for R and 270 for B. (270) Then, write the percents as a fraction. P= ( 1) 3 (270) Finally, multiply the numbers on the right side of the equality above. P = 90 18. Use the appropriate form of the percentage formula. Find B if P = 133 and R = 77 7 9 %. Next, write the division of two fractions in the right side as multiplication. B= 133 1 (9) 7 Then, reduce the fractions. B= 133 1 B= 19 1 (9) 7 (9) 1 Finally, multiply the numerators of the simplified fractions above to obtain the answer. B = 171 19. Use the appropriate form of the percentage formula. 80% of 90 is what number? To find the portion use the formula P = RB, where R is the rate and B is the base. Now write 80% as a decimal. 80% = 0.8 Rewrite the formula P = RB substituting 0.8 for R and 90 for B. P = 0.8 (90) Finally, multiply the numbers on the right side of the equality above. P = 72 20. A number increased from 780 to 1170. Find the percent of increase. First, find the amount of increase. Increase = new amount original amount = 1170 780 Substitute values. = 390 Subtract. To find the rate of increase or decrease, divide the amount of change by the original amount. amount of increase original amount Rate of increase = = 390 780 Substitute values. = 0.5 Simplify. Convert the rate of increase to a percent equivalent. 0.5 = 0.5 (100%) = 50% Multiply. Therefore, the percent of increase is 50%. 21. A number is decreased by 50% to 450. What is the original amount? First, Find the percentage of the original amount that the new amount represents. Rate represented by new amount = 100% - rate of decrease = 100% - 50% = 50% Substitute values. Subtract. Convert the rate represented by the new amount to its decimal equivalent. 50% = 50 100 = 0.5 Divide. Find the original amount. Original amount = reduced amount raterepresented by new amount = 450 0.5 = 900 Substitute values. Divide. Therefore, the original amount is 900. 22. The cost of a pound of mails increased from $2.46 to $ 2.57. What is the percent of increase to the nearest whole number percent? First, find the amount of increase. Increase = new amount original amount = $2.57 - $2.46 Substitute values. = $0.11 Subtract. To find the rate of increase or decrease, divide the amount of change by the original amount. amount of increase original amount Rate of increase = = $ 0.11 $ 2.46 Substitute values. = 0.0447 Simplify. Convert the rate of increase whole-number percent. 4.47% = 4% Therefore, the percent of increase is approximately 4%. 23. A worker is getting a 2.5% raise. His current salary is $39,298. How much will his raise be? To find the amount of increase, multiply the decimal or factional equivalent of the rate of change times the original or beginning amount. Amount of increase = percent of change * original amount = 2.5% ($39,298) = 0.025 ($39,298) = $982.45 Substitute the values. Write percent as a decimal. Multiply. Therefore, the amount of his raise will be $ 982.45. 24. An employee makes $11.81 per hour but is getting a 5% increase. What is his new wage per hour to the nearest cent? First, find the rate of the new amount, Use the formula given below. Rate of new amount = 100% + rate of increase = 100% + 5% = 105% Substitute. Add. To find the new amount, multiply the rate of the new amount by the original amount. New amount = rate of new amount * original amount = 105% ($11.81) = 1.05($11.81) Write percent as a decimal. = $12.40 Multiply. Therefore, the employees new wage is $12.40. 25. Carol Wynne bought a silver tray that originally cost $210 and was advertised at 70% off. What was the sale price of the tray? Find the rate of the new amount. For an increase, the new rate will be 100% + rate of increase. For a decrease, the new rate will be 100% - rate of decrease. The rate of the new amount is 30%. New amount = rate of new amount * original amount. New amount = 30% * ($210) Write the percent as a decimal. 30% * ($210) = 0.3 * ($210) Find the price. 0.3 * ($210) = $63 Thus, the sale price was $63. 26. 27. 28. 29. Weekly expenses of students talking a business mathematics class in the table. 77 a. Find the mean. b. Find the median. c. Find the mode. a. To obtain the mean value, first find the sum of expenses. The sum is 2231. Divide the sum by the number of students in the class. The resulting value is the mean. 2231 26 = 86 Thus, the mean is 86. b. To find the median of the scores, first arrange the value in order from the smallest to the largest. 40,54,60,67,75,77,78,78,79,80,81,84,86,86,86,88,89,91,92,93,97,97,98,100,105,170. Since 26 is an even number, the median is the average of the two middle numbers. The median is 86. c. To find the mode, look for the score with the greatest frequency. This score is the mode. The mode is 86. It occurs three times in the table. 30. Salaries for the research and development department are given as $ 48,345; $ 27,961; $42,573; $19,522; $32453; and $37,574, Find the mean, the median, and the mode of salaries. Since the number of values is even, there are two middle values, $32,453 and $37,574. Find the mean of the middle two values by dividing their sum by 2. $ 32,453+ $ 37,574 2 = $ 35,013.50 Thus, the median is $35,013.50 C. The mode is value or values that occur most frequently in a data set. If no value occurs more than once, then there is no mode for the data set. Recall the ordered arrangement, $19,522; $27,961; $32,453; $37,574; $42,573; $48,345. There are no values that occur more than once. Thus, there is no mode because no salary is listed more than once. 31. 32. The 7th Inning wants to group a collection of autographed photos by price ranges. The table with the prices is shown on the right. What percent of the collection is priced below $20? $3.41 $25.82 $9.72 $5.63 $37.49 $8.29 $13.23 $8.56 $6.53 $26.02 $9.77 $19.35 $9.11 $18.54 $17.47 $22.55 $36.64 $7.78 $4.75 $17.91 $46.28 $34.86 $19.11 $15.82 $6.64 $10.61 $42.12 $15.74 $47.66 $26.83 There are 20 prices that are below $20. The total number of prices is 30. To find the percent of prices below $20, First divide the number of such prices by the total number of prices. 20 30 = 0.67 Multiply the obtained ratio by 100% to get the required percent. 0.67 * 100% = 67% Thus, approximately 67% of the collection is price below $20. 33. A company wants to group a collection of autographed photos by price ranges. What percent of the collection is priced $40 or over? $2.50 $26.00 $7.50 $9.50 $32.50 $3.75 $14.78 $16.67 $8.25 $20.00 $1.19 $12.75 $7.50 $7.86 $10.00 $21.50 $35.00 $8.00 $25.00 $17.50 $43.00 $37.50 $12.50 $18.50 $6.75 $15.00 $48.00 $15.00 $45.00 $28.50 The number of photos in the interval $40 - $49.99 is 3. The total number of photos in the collection is 30. To find the percent of the collection priced $40 or over, divide the number of values in the $40 - $49.99 range by the total number in the collection. Percent = 3 30 = 0.1 Write as a percent. The portion or part is 3 and the base or total is 30. 1.1 = 10% 1.2Therefore, 10% of the collection is priced $40 or over. 34. The data shows the total number of employee medical leave days taken for on-the job accidents is the first six month of the year; 11, 7, 14, 8, 15, 11. Find the mean number of days taken for medical leave each month. Find the mean. Mean = of data values number of values = 11 +7+14+ 8+15+11 6 = 66 6 Find the sum in the numerator. Divide 66 by 6. 66 6 = 11 Thus, the mean number of days taken for medical leave each month is 11. 35. The data shows the total number of employee medical leave days taken for on-the job accidents is the first six month of the year; 15, 7, 21, 9, 23, 15. Find the standard deviation. First find the mean of the set of data. Mean = = of data values number of values 15+ 7+21+9+23+15 6 90 6 = Find the sum in the numerator. Divide by 6. 90 6 = 15 Next find the deviation of each value from the mean. Data values 15 Deviation from mean Data Value - Mean 15 15 = 0 7 15 = - 8 21 15 = 6 9 15 = -6 23 15 = 8 15 15 = 0 Square each deviation. Data values 15 Squares of the Deviations Deviation * Deviation (0)(0) = 0 (-8)(-8) = 64 (6)(6) = 36 (-6)(-6) = 36 (8)(8) = 64 (0)(0) = 0 Now find the variance by dividing the sum of the squared deviations by 1 less than the number of values in the data set. Variance = = = of squared deviations n1 0+64+36 +36+64+ 0 5 200 5 Divide 200 by 5. Find the sum in the numerator. 200 5 = 40 Finally find the standard deviation by taking the square root of the variance. S= 40 6.32 Thus, the standard deviation is about 6.32. 36. Find the trade discount on a computer that lists for $700 if a discount rate of 10% is offered. To solve this problem, use the following formula. Trade discount = single trade discount rate * list price Find the trade discount. Substitute known values into the formula. Trade discount = 10% ($700) = 0.1 ($700) Write the percent as a decimal. = $70 Multiply. Therefore, the trade discount is $70. 37. Find the net price of a computer that lists for $480 if a discount rate of 25% is offered. Trade discount = single trade discount rate * list price T = RL T = 25%. ($480) T = 0.25($480) T = $120 Find the net price of the computer. Net price = list price trade discount. N=LT N = $480 - $120 Substitute the list price and the trade discount. Subtract. N = $480 - $120 = $360 Thus, the net price of the computer is $360. 38. Calculate the trade discount for 20 boxes of computer paper if the unit price is $15.51 and single trade discount rate of 10% is allowed. First, find the list price of all boxes. List price of all boxes = number of boxes * unit price = 20 ($15.51) = $310.20 Multiply. To solve this problem, use the following formula. Trade discount = single trade discount rate * list price Find the trade discount for all boxes, Substitute known values into the formula. Trade discount = 10% ($310.20) = 0.1 ($310.20) Write the percent as a decimal. = $31.02 Multiply. Therefore, the trade discount is $31.02. 39. A company manages an electronic equipment store and has orderd 50 remote controlled color TVs for a special sale. The list price for each TV is $250 with a trade discount series of 7/9/4. Find the net price of the order by using the net decimal equipment. Find the complement of the first discount rate and write it as an equivalent decimal. 100% - 7% = 93% = 0.93 Subtract. write the percent as a decimal. Find the complement of the second discount rate and write it as an equivalent decimal. 100% - 9% = 91% = 0.91 Subtract. write the percent as a decimal. Find the complement of the third discount rate and write it as an equivalent decimal. 100% - 4% = 96% Subtract. = 0.96 write the percent as a decimal. Multiply the complements to find the net decimal equivalent. (0.93)(0.91)(0.96) = 0. To find the total list price of TVs multiply the number of TVs by the list price of each TV. 50($250) = $12,500 Find the total net price. Total net price = net decimal equivalent * total list price = 0. ($12,500) $10,155.60 40. One distributor lists ink-jet printers with 360 dpi and six scalable fonts that can print envelopes, labels, and transparencies for $175.55 with a trade discount series of 5/5/15. Another distributor lists the same brand and model printer at $220 with trade discount series of 5/15/15. Which is the better deal if all other aspects of the deal, such as shipping, time of availability, and warranty are the same or equivalent? Respectively Find the net decimal equivalent for the second deal. Net decimal equivalent = 0.95 (0.85)(0.85) Deal 2 = 0. Find the net price, rounded to the nearest cent for second deal. Net price for second deal = (0.)$220 Deal 2 $151.00 The first deal, $175.55 with the 5/5/15 discount series, is the better deal. 41. A man received an invoice dated March 9, with term 3/10, n/30 amounting to $520. He paid the bill on March 12. How much was the cash discount? The cash discount is a discount on the amount due on an invoice that is given for prompt payment. To find the cash discount, multiply the cash discount rate by the net price. Use the following formula. Cash discount = cash discount rate * net price The cash discount rate is 3% The net price is $520. Replace the terms with the values and perform the calculations. Cash discount = cash discount rate * net price = 3% ($520) = 0.03 ($520) Write the percent as a decimal. Multiply to get the cash discount. 0.03 ($520) = $15.60 Thus, the cash discount is $15.60. 42. A man gets an invoice for $470 with terms 4/10, 1/15, n/30. How much would he pay 5 days after the invoice data? To find the amount, multiply the net price by the complement of the cash discount rate. Use the following formula. Net amount = complement of cash discount rate * net price First, identify the cash discount rate. It is 4%. To find the complement of the cash discount rate, subtract the cash discount rate from the 100%. 100% - 4% = 96% Second, identify the net price. It is $470. Replace the terms with the known values and perform the calculations. Write the percent as a decimal. Net amount = complement of cash discount rate * net price = 96 %($470) = 0.96($470) Multiply to get the net amount. 0.96($470) = $451.20 Thus, the net amount is $451.20. 43. A man gets an invoice for $430 with terms 2/10, 1/15, n/30. How much would he pay 23 days after the invoice data? The 2/10 means a 2% cash discount rate may be applied if the bill is paid within 10 days of the invoice data. The 1/15 means that a 1% cash discount rate may be applied if the bill paid within 15 days of the invoice date. The n/30 means that the full amount or net amount of the bill is due within 30 days. No cash discount is allowed 23 days after the invoice date, because the invoice is not being paid within 10 or 15 days. So, he would pay $430. 44. Kariem salaam is directing the accounts payable office and is training a new accounts payable associate. They are processing an invoice for a credenza that is dated August 19 in the amount of $388.18. The delivery ticket for the credenza is dated August 20. If the sales terms indicated on the invoice are 3/10 ROG, how much needs to be paid if the bill is paid on September 7? The terms 3/10 ROG mean that a 3% discount is allowed on the bill if it is paid within 10 days of the receipt of goods. No discount is allowed if the bill is paid on September 7, since the bill is not being paid within 10 days of the receipt of goods. Thus, $388.18 is due if the bill is paid on September 7. 45. A man has an invoice for a complete computer system for $3,941.12. The invoice shows terms of 4/10, 3/15, n/30. He can afford pay $2,600 within 10 days of the date on the invoice and the remainder within the 30 day period. How much should be credited to the account for the $2,600 payment, and how much is still due? First, divide the amount of the partial payment by the complement of the discount rate to find the amount credited. Use the following formula. Amount credited = payment complement of cash discount rate Identify the cash discount rate. It is 4% To find the complement of the discount rate, subtract the cash discount rate from 100% 100% - 4% = 96% Write the percent as a decimal. 96% = 0.96 Identify the partial payment with the known values and perform the calculations. payment complement of cash discount rate Amount credited = = $ 2,600 0.96 $2,708.33 Thus, the amount credited for the $2,600 payment is $2,708.33. Second, to find the outstanding balance, subtract the amount credited from the net price. Use the following formula. Outstanding balance = net price amount credited Identify the net price. It is $3,941.12. Replace the terms with the known values and perfrom the calculation. Outstanding balance = $3,941.12 - $2,708.33 = $1,232.79 Thus, the outstanding balance is $1,232.79. 46. Selling price = $39.99; Markup = 13.99. Find the cost. The unknown amount is the cost, to find the cost, use the formula given below. Cost = selling price markup C = S - M Substitute known values. C = S-M = 39.99 13.99 Substitute without $ symbol. = 26 Subtract. Thus, the cost is $26. 47. Markup = $80; Rate of markup based on cost = 82%. a. Find the cost. b. B. Find the selling price. Thus, the cost is $97.56. b, To find the selling price, use the formula given below. Selling price = cost + markup S =C + M Substitute known values. S=C+M = 97.56 + 80 Substitute without $ symbol. = 177.56 Add Thus, the selling price is $177.56. 48. Cost = $70; Selling price = $168. a. Find the markup. b. Find the rate of markup based on cost. = M C M% = $ 98 $ 70 M% = M% (100%) (100%) 1.4 (100%) Change to percent equivalent. M % = 1.4 (100%) M % = 140% Thus, the percent of markup based on cost is 140%. 49. A HDTV sells for $365 and has a 40% markup based on cost. Find the cost and markup. S S = M% $ 365 140 = Substitute the value of S and S% $ 365 = 1.40 Change the percent to its decimal equivalent. $260.71 Divide and round to the nearest cent. Find the markup. M = S C $365 - $ 260.71 $104.29 Substitute the value of S and C Subtract. Thus, the cost is $260.71 and the markup is $104.29. 50. Cost = $51; selling price = $60. Find the rate of markup based on the selling price. First find the amount of markup using the following formula. Markup = Selling price - Cost M = S Substitute known values. M=SC M = 60 51 - C M=9 Subtract. Next find the rate of markup based on selling price using the following formula. Rate of markup based on selling price = M% = M S Markup selling price * 100% * 100% Substitute known values into the previous formula. M% = M S * 100% M% = 9 60 * 100% M% = 0.15 * 100% Divide. Multiply by 100 to change the decimal to the percent equivalent. M% = 0.15 * 100% M% = 15% Thus, the rate of markup is 15%. 51. An item sells for $56 and is reduced to sell for $35. Find the markdown amount and the rate of markdown. To find the markdown, use the formula given below. Markdown = original selling price reduced price. Substitute known values. M=SN = $56 - $35 = $21 Subtract. Thus, the markdown is $21. To find the rate of markdown, use the formula given below. M% = M S * 100% Substitute known values. M% = M S M% = $ 21 $ 56 * 100% M% = $ 21 $ 56 * 100% * 100% Divide. M% = 37.5% Thus, the rate of markdown is 37.5%. 52. Selling price = $800; reduced (New) price = $550. Find the markdown amount the rate of markdown. To find the markdown, use the formula given below. Markdown = original selling price reduced price Substitute known values. M = S N = $800 - $550 = $250 Subtract. Thus, the markdown is $250. To find the rate of markdown, use the formula given below. M% = M S * 100% Substitute known values. M% = M S M% = $ 250 $ 800 * 100% M% = $ 250 $ 800 * 100% * 100% Divide. M% 0.313 (100%) Multiply. M% = 0.313 (100) M% = 31.3% Thus, the rate of markdown is 31.3%. 53. How much interest will have to be paid on a loan of $7,910 for two years at a simple interest rate of 5.9% per year? To find the interest, use the simple interest formula I = PRT Where I is the interest, P is the principal, R is the rate, and T is the time. Principal is the amount of money borrowed or inverted. Identify the principal. P = $7,910 Rate is the percent of the principal paid as interest per time period. Identify the rate. R = 5.9% Time is the number of days, months, or years that money is borrowed or invested. Identify the time. T = 2 years Substitute values determined above for P , R, and T in the simple interest formula. I = $7,910(5.9%)(2) = $7,910(0.059)(2) Write 5.9% as a decimal. Multiply. $7,910 (0.059)(2) = $933.38 Thus, the interest on the loan is $933.38. 54. Convert to years, expressed in decimal form to the nearest hundredth. 5 months To convert to years, expressed in decimal form, divide the number of months by the number of months in a year. First, write the fraction to convert to years. The numerator is 5. The denominator is 12. So, convert to years. 5 month = 5 12 year To write the fraction in decimal form, divide the numerator by the denominator obtained above. 5 12 = 0.42 Thus, 5 months is 0.42 year. 55. 56. A loan made on March 16 is due September 4 of the following year. Find the exact time for the loan is a non kap year and leap year. To find the due date use the table, Sequential Numbers for Dates of the Year, to transform the given dates to the numbers of these days of the year. Then find their difference. Lastly, add the leap day to the result. March 16 is the 75th day. Subtract 75 from 365. 365 75 = 290 So, there are 290 days from March 16 to December 31. September 4 is the 247th day. Add 290 and 247 to find the exact time of the loan. 290 + 247 = 537 Finally, find the exact time in a leap year. Since Feb. 29 is beginning and due dates, add 1 to the non leap year total. 537 + 1 = 538 Thus, the exact time is 537 days in a non leap year and 538 days in a leap year. 57. A loan is made on January 17 and has a due date of October 20 during a leap year. Find the exact time if the loan. To find the due date use the table, Sequential Numbers for Dates of the Year, to transform the given dates to the numbers of these days of the year. January 17 is the 17th day. October 20 is the 293th day. Subtract 17 from 293. 293 17 = 276 Since Feb. 29 is between the beginning and due dates, add I to the obtained value. 276 1 = 276 Thus, the exact is 277 days in a leap year. 58. A loan is made on March 20 for 180 days. Find the due date. To find the due date use the table, Sequential Numbers for Dates of the Year, to transform the given dates to the numbers of these days of the year. March 20 is the 79th day. Find the number of the due day. 79 + 180 = 259 Transform the obtained value to the date. The correct date is September 16. Thus, the due date is September 16. 59. A man marks a simple discount note with a face value of $2,300. A team of 140 days, and a 9% discount rate, Find the discount. (Use the bankers rule.) T= 140 360 Substitute the known values into the equation. P is $2,300. R is 0.09, and T is 140 360 . Perform the operations. I = $2,300 (0.09) ( 140 ) 360 = $2,300(0.035) Multiply. Multiply. 2,300 (0.09) = $81 Thus, the discount is $81. 60. Find the discount and proceeds on a $3,230 face-value note for three months if the discount rate is 9.2%. (Use the bankers rule.) To find the bank discount, use the formula I = PRT Where I is the bank discount, or the interest, P is the face value, R is the discount rate. and T is the time. The face value is the amount borrowed. Identify the face value. P = $3,230 Identify the discount rate. R = 9.2% Write the percent as a decimal. R = 0.092 Identify the time. T = 3 months Convert the time to days. T = 90 days Use the bankers rule. Converts T to years by dividing by 360. T= 90 360 Replace the letters with the known values. P is $3,230, R is 0.092, and T is 90 360 . Perform the operations. I = $3,230 (0.092) 90 ( 360 ) = $3,230(0.023) Multiply. Multiply. $3,230 (0.023) = $74.29 Thus, the discount is $74.29. To find the proceeds, use the formula A=PI Where A is the proceeds, P is the face value, and I is the bank discount, or the interest. Replace the letters with the known values. P is $3,230, and I is $74.29. Perform the operations. A = $3,230 - $74.29 = $3,155.71. Thus, the proceeds are $3,155.71. 61. Find the maturity value of the undiscounted promissory note states that Phillip Esterey borrowed $1,000 for a period of 10 months ordinary interest at 8%.the date of the note was July 21, 2008.The maturity date was 21. Write the sequential numbers for the days of the year, presented in the problem statement. July 21=day 202 May 21=day 141 The maturity date was May 21,2009.This year was not a leap year,thus 141 days of the period of the loan were in the year 2009.The last day of year 2008 was December 31 which has a sequential number 365-202=163 days of the period of the lone were in the year 2008. The whole period of the loan was 163+141=304 days. Find the interest. $1,000(0.08) ( 304 ) 360 = $67.56 Find the maturity value of the note. $1,000+$67.56+$1067.56 Thus, the maturity value of the undiscounted promissory note is $1,067.56. 62. A bank made a farmer a loan of $1,000 at 18% for three years compounded annually. Find the future value and the compound interest paid on the loan. Compare the compound interest with simple interest for the same period. The compound interest is given by the formula below. Compound interest = future value original principal Therefore, to begin with we need to find the future value. Recall that the future value is the last end of principal. To find the first end-of-period principal multiply the original principal by the sum of 1 and the period interest rate. First end of period principal = original principal * (1 + period interest rate) For each remaining period in turn, find the next end- of-period principal: Multiply the previous end-of-period principal by the sum of 1 and the period interest rate. End of period principal = previous End of period principal * (1 + period interest rate) Since the loan is for three years compounded annually, the loan is compounded over three periods. Find the first End of period principal. First End of period principal = $1,000(1 + 0.18) = $1,000(1.18) Perform the additional = $1,180 Multiply. Find the second End of period principal. Second End of period principal = $1,180 (1 + 0.18) = $1,180(1.18) = $1,392.4 Perform the addition. Multiply. Find the third End of period principal. Third End of period principal = $1,392.4 (1 + 0.18) = $1,392.4(1.18) $1,643.03 Perform the addition. Multiply. Thus, the future value is approximately $1,643.03. Calculate the compound interest = $1,643.03 - $1,000 = $643.03 Subtract. Now, find the simple interest. For this use the following formula. Simple interest = original principal * period interest rate * number of periods Calculate the simple interest. Simple interest = $1000(0.18)(3) = $540 Multiply. Compare the compound interest and the simple interest. Compound interest = $643.03 - $540 = $103.03 Subtract. Thus, the compound interest is approximately $103.03 more than the simple interest. 63. Tom bond borrowed $6,100 at 8 1 2 % for three years compounded annually. What is the compound amount of the loan and how much interest will he play on the loan? The compound interest is given by the formula below. Compound interest =compound amount-original principal, Therefore, to begin with we need to find the compound amount. Recall that the compound amount is the last end of-period principal. To find the first end-of-period principal multiply the loan by the sum of 1 and the period interest rate. First end-of-period principal = loan * (1+period interest rate) For each remaining period in turn, find the next end-of-period principal: Multiply the previous end-of-period principal by the sum of 1 and the period interest rate. End-of-period principal = previous end-of-period principal * (1 + period interest rate) Since the loan is for three years compound annually, the loan is compounded over three periods. Find the first end-of-period principal. First end-of-period principal = $6,100(1+0.085) =$6,100(1.085) performs the addition =$6,618.50 Multiply. Find the second end-of-period principal Second end-of-period principal= $6,618.50(1+0.085) = $6,618.50(1.085) $7,181.07 Perform the addition. Multiply Find the third end-of-period principal. Third end-of-period principal = $7,181.07(1+0.085) = $7,181.07(1.085) $1,791.46 Multiply. Thus the future value is approximately $7,791.46. Calculate the compound interest. Compound interest = $7,791.46 - $6,100 = $1691.46 Subtract. Thus, the compound interest is approximately $1691.46. 64. Perform the addition. Margaret Hillman invested $4,000 at 2.6% compounded quarterly for one year. Find the future value and the interest earned for the year. Use the simple interest formula method. To find the future value, determine the number of interest periods and the period interest rate. The number of interest periods is 4, because interest is compounded quarterly and the period of investment is one year. To find the period interest rate, use the following formula. annualinterest rate number of interest periods per year Period interest rate = Find the period interest rate. 2.6 4 = 0.65% The period interest rate is 0.65% or 0.0065. Find the first end of period principal by multiplying the original principal by the sum of 1 and the period interest rate. End of period principal = previous end-of-period principal * (1 + period interest rate) = $4,000(1 + 0.0065) = $4,026.00 For each remaining period in turn, find the next end-of-period principal by multiplying by previous end-of-period principal by the sum of 1 and the period interest rate. Find the second end of period principal. End-of-priod principal = previous end-of-period principal * (1 + period interest rate) = $4,026.00(1 + 0.0065) = $4,052.17 Find the third end of period principal. End-of-period principal = previous end-of-period principal * (1 + period interest rate) = $4,052.17(1 + 0.0065) = $4,078.51 Find the Fourth End-of-period principal. End-of-period principal = previous end-of-period principal * (1 + period interest rate) = $4,078.51(1 + 0.0065) = $4,105.02 The last end of period principal is the future value. Thus, the future value is $4,105.02. Subtract the original principal from the future value to find the compound interest. Compound interest = future value original principal = $4,105.02 - $4,000 $105.02 Thus, the compound interest is $105.02 and the future value is $4,105.02. 65. Find the effective interest rate for a loan for three years compounded semiannually at an annual rate of 6%. Use the formula period interest rate = annualinterest rate number of interest periods per year . Find the period interest rate. 6 2 = 3% The loan is compounded semiannually, which means there are 2 interest periods per year. The table value for 3% interest rate and periods is 1.06090. Subtract 1 from the table value and multiply by 100%. Effective rate = (1.06090 1)(100%) = (0.06090)(100%) = 6.09% Thus, the effective interest rate 6.09% 66. Ross land has a loan of $8,500 compounded quarterly for three years at 10%. What is the effective interest rate for the loan? Use the formula period interest rate = interest rate. annualinterest rate number of interest periods per year . Find the period 12 4 = 3% The loan is compounded quarterly, which means there are 4 interest period per year. The table value for 3% interest rate and 4 periods is 1.12551. Subtract 1 from the table value and multiply by 100% Effective range = (1.12551 - 1)(1010%) = (0.12551)(100%) = 12.55% Thus, the effective interest rate is 12.55%. 67. Compute the amount of money to be set aside today to ensure a future value of $5,500 in one year if the interest rate is 6.5% annually, compounded annually. The amount to be set aside today is called the present value. To find the present value, divide the future value by the sum of 1 and the decimal equivalent of the annual interest rate. Convert the annual interest rate to the decimal notation and add it to 1. 1.0 + 0.065 = 1.065 The present value is equal to the future value div by 1,065. Find the present value. $ 5,000 1.065 $5,164.32 Thus, the amount of money to be set aside is $5,164.32. 68. How much should Linda Bryan set aside now to buy equipment that costs $4,500 in one year? The current interest rate is 1.05% annually, compounded annually. The amount to be set aside today is called the present value. To find the present value, divide the future value by the sum of 1 and the decimal equivalent of the annual interest rarte. Convert the annual interest rate to the decimal notation and add it to 1. 1.0 + 0.0105 The present value is equal to the future value divided by 1.10105. Find the present value. $ 4,500 1.0105 $4,453.24 Thus, the amount of money to be set aside is $4,453.24. 69. Ronnie Cox has just inherited $27,000. How much of this money should be set aside today to have $26,000 to pay cash for a Venture Van, which he plans to purchase in one year? He can invest at 1.5% annually, compounded annually. The amount to be set aside today called the present value, divides the future value bu the sum of 1 and the decimal equivalent of the decimal equivalent of the annual interest rate. Convert the annual interest rate to the decimal notation and add it to 1. 1.0 + 0.015 = 1.015 The present value is equal to the future value divided by 1.015. Find the present value. $ 26,000 1.015 $25,615.76 Thus, the amount of money to be set aside is $25,615.76. 70. Rosa Burnett needs $1,500 in three years to make the down payment on a new car. How much must she invest today if she receives 1.5% interest annually, compounded annually? The number of interest periods per year is 1. Find the total number of interest periods. Multiply the time period, in years, by the number of interest periods per year. Interest periods = number of years * number of interest periods per year = 3(1) =3 Find the period interest rate. Divide the annual interest rate by the number of interest periods per year. Period interest rate = annualinterest rate number of interest periods per year = 1.5 1 = 1.5% Using the table, select the periods row that corresponds to the number of interest periods. Select the rate-per-period column that corresponds to the period interest rate. Locate the value in the cell where the periods row intersects the rate-per-period column. This value is the present value of $1.00 and is equal to 0.95632. Multiply the present value of $1.00 by the value of the amount of money desired to obtain the present value. 0.95632($1,500) = $1,434.48 Therefore, she must invest $1,434.48. 71. Prepare a balance sheet for the bakery for December 31, 2012. The company assets include cash, $2,035, account receivable, $4,131, and merchandise inventory, $2,401. The liabilities include accounts payable, $3,653, wages payable, $1,727. The owners capital is $3,187. To find total assets, add all the assets to each other. Total assets = $2,035 + $4.131 + $2,401 = $8,567 Add. To find total liabilities, add all the liabilities to each other. Total liabilities = $3,653 + $1,727 = $5,380 Add. To find total liabilities and owners equity, add them. Recall that the words used to mean the same thing as owners equity are stockholders equity, capital, proprietorship, and net worth. Owners equity is $3,187. Find total liabilities and owners equity. Total liabilities and owners equity = $5,380 + $3,187 Prepare the balance sheet. Bakery Balance sheet December 31,2012 Assets Cash Accounts receivable Merchandise inventory Total assets $2,035 4,131 2,401 $8,567 Liabilities Accounts payable Wages payable Total liabilities $3,653 1,727 $5,380 Owners equity The owners capital Total liabilities and owners equity 3,187 $8,567 72. Prepare a balance sheet for the nursery for December 31, 2012. The company assets include cash, $8,766, account receivable, $7,823, and merchandise inventory, $18,050. The liabilities include accounts payable, $18,247, wages payable, $3,460. The owners capital is $20,932. To find total assets, add all the assets to each other. Total assets = $8,766 + $7,823 + $18,050 = $34,639 Add. To find total liabilities, add all the liabilities to each other. Total liabilities = $10,247 + $3,460 = $13,707 Add. To find total liabilities and owners equity, add them. Recall that the words used to mean the same thing as owners equity are stockholders equity, capital, proprietorship, and net worth. Owners equity is $20,932. Find total liabilities and owners equity. Total liabilities and owners equity, Total liabilities and owners equity = $13,707 + $20,932. = $34,639 Add. Nursery Balance sheet December 31,2012 Assets Cash Accounts receivable Merchandise inventory Total assets $8,766 7,823 18,050 $34,639 Liabilities Accounts payable Wages payable Total liabilities $10,247 3,460 $13,707 Owners equity The owners capital Total liabilities and owners equity 20,932 $34,639 73. Complete the vertical analysis on the balance sheet for the bakery for 2012. To find the percent of total assets for some item, divide the amount of the item by total assets then multiply by 100% to record the result as a percent. Determine the total assets from the balance sheet. Total assets are $8,573. Find the percent for cash. Percent = 1,905 8,573 * 100% = 22.2% Find the percent for accounts receivable. Simplify. Percent = 4,260 8,573 * 100% = 49.7% Simplify. Find the percent for merchandise inventory. Percent = 2,408 8,573 * 100% = 28.1% Simplify. Find the percent for assets. Percent = 8,573 8,573 * 100% = 100% Simplify. Find the percent for account payable. Percent = 3,483 8,573 * 100% = 40.6% Simplify. Find the percent for wages payable. Percent = 1,866 8,573 * 100% = 21.8% Simplify. Find the percent for total liabilities. Percent = 5,349 8,573 * 100% = 62.4% Find the percent for the owners capital. Simplify. Percent = 3,224 8,573 * 100% = 37.6% Simplify. Find the percent for total liabilities and owners equity. Percent = 8,573 8,573 * 100% = 100% Simplify. Complete the balance sheet. Nursery Balance sheet December 31,2012 Amount Percent $1,905 4,260 2,408 $8,573 22.2% 49.7% 28.1% 100% $3,483 1,866 $5,349 40.6% 21.8% 62.4% 3,224 $8,573 37.6% 100% Assets Cash Accounts receivable Merchandise inventory Total assets Liabilities Accounts payable Wages payable Total liabilities Owners equity The owners capital Total liabilities and owners equity 74. Complete the vertical analysis on the balance sheet for the nursery for 2012. To find the percent of total assets for some item, divide the amount of the item by total assets then multiply by 100% to record the result as a percent. Determine the total assets from the balance sheet. Total assets are $34,271. Find the percent for cash. Percent = 8,400 34,271 * 100% = 24.5% Simplify. Find the percent for accounts receivable. Percent = 7,864 34,271 * 100% = 22.9% Simplify. Find the percent for merchandise inventory. Percent = 18,007 34,271 * 100% = 52.5% Simplify. Find the percent for assets. Percent = 34,271 34,271 * 100% = 100% Simplify. Find the percent for account payable. Percent = 3,483 8,573 * 100% = 40.6% Find the percent for wages payable. Simplify. Percent = 3,733 34,271 * 100% = 10.9% Simplify. Find the percent for total liabilities. Percent = 13,133 34,271 * 100% = 38.3% Simplify. Find the percent for the owners capital. Percent = 21,138 34,271 * 100% = 61.7 % Simplify. Find the percent for total liabilities and owners equity. Percent = 34,271 34,271 = 100% * 100% Simplify. Complete the balance sheet. Nursery Balance sheet December 31,2012 Amount Percent Assets Cash Accounts receivable Merchandise inventory Total assets $8,400 4,864 18,007 $34,271 24.5% 22.9% 52.5% 100% $9,400 3,733 $13,133 27.4% 10.9% 38.3% 21,138 $34,271 61.7% 100% Liabilities Accounts payable Wages payable Total liabilities Owners equity The owners capital Total liabilities and owners equity 75. Complete the income statement for Sitha Ross Oriental Groceries for the years 2011 and 2012. First lets find gross profit for 2012. Gross profit = net sales cost of goods sold = $98,265 - $81,567 = $16,698 Analogously find gross profit for 2011. Gross profit = $20,211 Now find net income for 2012. Net income = gross profit operating expenses = $16,698 - $3,967 = $12,731 Analogously find net income statement. Sitha Ross Oriental Groceries Income statement For the years Ending June 30,2011 and $98,265 $91,789 Cost of goods sold 81,567 71,578 Gross profit 16,698 20,211 3,967 3,543 $12,731 $16,668 Net sales Operating expenses Net income 76. Complete the portion for July 31,2011, for the income statement shown for Miss Muffins Bakery using the given information: gross sale, $34,568; returns and allowances, $340; cost of beginning inventory, $16,342; cost of purchases, $26,599; cost of ending inventory, $21,683; total operating expenses, $2,979. Compute net sales, cost of goods sold, gross profit, and net income. First lets find the net sales. Net sales = gross sale returns and allowances = $34,568 - $340 $34,228 Now find the net cost of goods sold. Cost of goods sold = cost of beginning inventory + cost of purchase cost of ending inventory = $16,342 + $26,599 - $21,683 = 21,258 Then find the gross profit. Gross profit = net sales cost of goods sold = $34,228 - $21,258 = $12,970 Finally, find the net income. Net income = gross profit operating expenses = $12,970 - $2,979 = $9,991 Now complete the income statement. Miss Muffins Bakery Comparative Income statement for the Months Ending July 31, Gross sales $34,568 Returns and allowances 340 Net sales 34,228 Cost of beginning inventory 16,342 Cost of purchases 26,599 Cost of ending inventory 21,683 Cost of goods sold 21,258 Gross profit 12,970 Total operating expenses 2,979 Net income $9,991 77. Find the current ratio for Georges business and the current ratio for Joses business, given the following information: George Jose Current assets $30,000 Current liabilities - 7000 Working capital $23,000 $820,000 - 7, 97,000 $23,000 To calculate the ratios, use the following formula. Georges (Joses) current ratio = Georges current ratio = Joses current ratio = 30,,000 797,000 current assets current liabilities = 4.29. = 1.03. 78. Find the acid-test ratio for a business if the balance sheet shows the following amounts: cash, $32,429; receivables, $13,029; marketable securities, $0; current liabilities, $20,395. The acid-test ratio is given by the following formula. Acid-test ratio = quick current assets current liabilities The acid-test ratio uses only the quick current assets, those assets that can be readily exchanged for cash; marketable securities, accounts receivable, and notes receivable. Substitute for the quick current assets and current liabilities in the formula for acid-test ratio. Acid-test ratio = $ 32,429+ $ 13,029 $ 20,395 Simplify the numerator. Acid-test ratio = $ 32,429+ $ 13,029 $ 20,395 = $ 45,458 $ 20,395 Acid-test ratio = $ 45,458 $ 20,395 Find the ratio. Add 2.23 Divide. Therefore, the acid-test ratio is approximately 2.23. 79. Find the operating ratio for Sols Dry Goods if the income statement for the month shows net sales, $14500; cost of goods sold, $5500; gross profit, $6000; operating expenses, $2500; net income, $2500.Expenses results to the nearest tenth of a percent. To calculate the ratio, use the following formula. Operating ratio = cost of goods sold + operating expenses net sales Operating ratio = 5500+ = 0.552 = 55.2% .100%