ACG 4101 Exam 2
Simple Interest Formula - answer Initial Investment x Interest Rate x Period of time
(x/12)
Compound Interest - answer includes interest on both principle and interest
accumulated in previous periods. i.e. semiannually, quarterly, monthly
Cindy invested $1,000 in a savings account paying 10% interest compounded twice a
year. What will be her investment balance at the end of the year? What is the effective
annual interest rate? - answer Divide 10% by 2 to make it 5% interest (annual rate
divided by 2 periods of 6 months).
Initial deposit after 6 months: 1,000 x 5% = 50
End of year 1: 1,050 x 5% = 52.50
Total balance after 1 year: 1,102.50
Single Cash Flow Formulas
- Future Value
- Present Value - answer- Future Value = PV x FV $ Factor
- Present Value = FV x PV $ Factor
- Future value entrails the addition of interest
- Present value entails the removal of interest
Cindy invested $1,000 in a savings account for 3 years paying 10% interest
compounded annually. What can she receive at the end of year 3? - answerFV = PV x
FV $ Factor
FV = 1,000 x 1.331 (from table)
FV = 1,331
or...
1,000 x 1.10 [1.00+.10] then multiply it be 3 years
1,000 x 1.10 x 1.10 x 1.10 = 1,331
What is the present value of 1,331 received at the end of 3 years (10% annual
compounding interest)? - answerPV = FV x PV $ Factor
PV = 1,331 x .75131
PV = 1,000
The Stridewell Wholesale Shoe Company recently sold a large order of shoes to
Harmon Sporting Goods. Terms of the sale require Harmon to sign a noninterest-
bearing note of $60,500 w/payment due in 2 years. What is the price of the shoes?
Assume the market interest rate is 10%. - answerPV = FV x PV $ Factor
,PV = 60,500 x .8265
PV = 50,000
The Versa Tile Company purchased a delivery truck on February 1, 2016. The
agreement required Versa Tile to pay the purchase price of $44,000 on February 1,
2017. Assuming an 8% rate of interest, to calculate the price of the truck Versa Tile
would multiply $44,000 by the:
a. future value of an ordinary annuity of $1.
b. present value of $1
c. present value of an ordinary annuity of $1
d. future value of $ - answerb
PV = FV x PV $ factor
PV = 44,000 x PV $ Factor
Turp and Tyne Distillery is considering investing in a two-year project. The company's
required rate of return is 10%. The present value of $1 for one period at 10% is .909
and .826 for two periods at 10%. The project is expected to create cash flows, net of
taxes, of $240,000 in the first year, and $300,000 in the second year. The distillery
should invest in the project if the project's cost is less than or equal to:
a. 540,000
b. 490,860
c. 465,960
d. 446,040 - answerc
PV = 240,000 x .909
PV = 218,160
PV = 300,000 x .826
PV = 247,800
218,160 + 247,800 = 465,960
Annuity
- Ordinary Annuity
- Annuity Due - answerA series of cash flows of same amount received or paid e/period.
- Ordinary A.: cash flow occurs at the end of e/period. The first cash flow is made one
compounding period after the date on which agreements begins. The final cash flow
takes place on the last day covered by the agreement.
- Annuity D.: cash flow occurs at the beginning of e/period. First payment is made on
the first day of the agreement. And the last payment is made 1 period before the end of
the agreement.
Valuing Annuity
- Future Value of equal cash flows
- Present Value of equal cash flows - answer- Future Value = Ann x FV Ann Factor. (If
lump sum occurs at the end or after annuity payments. o o o O)
, - Present Value = Ann x PV Ann Factor. (If lump sum occurs 1st or before annuity
payments. O o o o )
Sally Rogers wants to accumulate a sum of money to pay for graduate school. Rather
than investing a single amount today that will grow to a future value, she decides to
invest $10,000 a year over the next 3 years in a savings account paying 10% interest
compounded annually. She decides to make the 1st payment to the bank 1 year from
today. How much will Sally get at the end of the 3 years? - answerLooking for FV b/c
you are building up to a lump sum. Ordinary annuity b/c she wants to see what she gets
at the end of the period.
FVA = Ann x FV Ordinary Ann Factor
FVA = 10,000 x 3.31
FVA = 33,100
Sally Rogers wants to accumulate a sum of money to pay for graduate school. She
wants to invest a single amount today in a savings account earning 10% interest
compounded annually that is equivalent to investing $10,000 at the end of e/of the next
3 years. How much does she need to invest today? - answerLooking for PV b/c she
needs to know what she's investing today.
Ordinary Annuity b/c she's investing at the end of e/period.
PVA = Annuity x PV Ordinary Ann Factor
PVA = 10,000 x 2.48685
PVA = 24,868
Justin Investor wants to calculate how much money he needs to deposit today into a
savings account that earns 4% in order to be able to withdraw $6,000 at the end of e/of
the next 5 years. He should use which present value concept?
a. present value of $1 for 5 periods
b. future value of an annuity due $1 for 5 periods
c. present value of an ordinary annuity of $1 for 5 periods
d. future value of $1 for 5 periods - answerc
He's looking for present value "money he needs to deposit today".
Ordinary annuity b/c he wants to withdraw at the end of e/period.
The Stinch Fertilizer Corporation wants to accumulate $8,000,000 for plant expansion.
The funds are needed on January 1, 2021. Stinch intends to make 5 equal annual
deposits in a fund that will earn interest at 7% compounded annually. The first deposit it
to be made January 1, 2016. Present value and future value facts are as follows:
What is the amount of the required annual deposit?
a. 1,300,813
b. 1,391,304
c. 1,951,220
d. 1,704,000 - answera
Simple Interest Formula - answer Initial Investment x Interest Rate x Period of time
(x/12)
Compound Interest - answer includes interest on both principle and interest
accumulated in previous periods. i.e. semiannually, quarterly, monthly
Cindy invested $1,000 in a savings account paying 10% interest compounded twice a
year. What will be her investment balance at the end of the year? What is the effective
annual interest rate? - answer Divide 10% by 2 to make it 5% interest (annual rate
divided by 2 periods of 6 months).
Initial deposit after 6 months: 1,000 x 5% = 50
End of year 1: 1,050 x 5% = 52.50
Total balance after 1 year: 1,102.50
Single Cash Flow Formulas
- Future Value
- Present Value - answer- Future Value = PV x FV $ Factor
- Present Value = FV x PV $ Factor
- Future value entrails the addition of interest
- Present value entails the removal of interest
Cindy invested $1,000 in a savings account for 3 years paying 10% interest
compounded annually. What can she receive at the end of year 3? - answerFV = PV x
FV $ Factor
FV = 1,000 x 1.331 (from table)
FV = 1,331
or...
1,000 x 1.10 [1.00+.10] then multiply it be 3 years
1,000 x 1.10 x 1.10 x 1.10 = 1,331
What is the present value of 1,331 received at the end of 3 years (10% annual
compounding interest)? - answerPV = FV x PV $ Factor
PV = 1,331 x .75131
PV = 1,000
The Stridewell Wholesale Shoe Company recently sold a large order of shoes to
Harmon Sporting Goods. Terms of the sale require Harmon to sign a noninterest-
bearing note of $60,500 w/payment due in 2 years. What is the price of the shoes?
Assume the market interest rate is 10%. - answerPV = FV x PV $ Factor
,PV = 60,500 x .8265
PV = 50,000
The Versa Tile Company purchased a delivery truck on February 1, 2016. The
agreement required Versa Tile to pay the purchase price of $44,000 on February 1,
2017. Assuming an 8% rate of interest, to calculate the price of the truck Versa Tile
would multiply $44,000 by the:
a. future value of an ordinary annuity of $1.
b. present value of $1
c. present value of an ordinary annuity of $1
d. future value of $ - answerb
PV = FV x PV $ factor
PV = 44,000 x PV $ Factor
Turp and Tyne Distillery is considering investing in a two-year project. The company's
required rate of return is 10%. The present value of $1 for one period at 10% is .909
and .826 for two periods at 10%. The project is expected to create cash flows, net of
taxes, of $240,000 in the first year, and $300,000 in the second year. The distillery
should invest in the project if the project's cost is less than or equal to:
a. 540,000
b. 490,860
c. 465,960
d. 446,040 - answerc
PV = 240,000 x .909
PV = 218,160
PV = 300,000 x .826
PV = 247,800
218,160 + 247,800 = 465,960
Annuity
- Ordinary Annuity
- Annuity Due - answerA series of cash flows of same amount received or paid e/period.
- Ordinary A.: cash flow occurs at the end of e/period. The first cash flow is made one
compounding period after the date on which agreements begins. The final cash flow
takes place on the last day covered by the agreement.
- Annuity D.: cash flow occurs at the beginning of e/period. First payment is made on
the first day of the agreement. And the last payment is made 1 period before the end of
the agreement.
Valuing Annuity
- Future Value of equal cash flows
- Present Value of equal cash flows - answer- Future Value = Ann x FV Ann Factor. (If
lump sum occurs at the end or after annuity payments. o o o O)
, - Present Value = Ann x PV Ann Factor. (If lump sum occurs 1st or before annuity
payments. O o o o )
Sally Rogers wants to accumulate a sum of money to pay for graduate school. Rather
than investing a single amount today that will grow to a future value, she decides to
invest $10,000 a year over the next 3 years in a savings account paying 10% interest
compounded annually. She decides to make the 1st payment to the bank 1 year from
today. How much will Sally get at the end of the 3 years? - answerLooking for FV b/c
you are building up to a lump sum. Ordinary annuity b/c she wants to see what she gets
at the end of the period.
FVA = Ann x FV Ordinary Ann Factor
FVA = 10,000 x 3.31
FVA = 33,100
Sally Rogers wants to accumulate a sum of money to pay for graduate school. She
wants to invest a single amount today in a savings account earning 10% interest
compounded annually that is equivalent to investing $10,000 at the end of e/of the next
3 years. How much does she need to invest today? - answerLooking for PV b/c she
needs to know what she's investing today.
Ordinary Annuity b/c she's investing at the end of e/period.
PVA = Annuity x PV Ordinary Ann Factor
PVA = 10,000 x 2.48685
PVA = 24,868
Justin Investor wants to calculate how much money he needs to deposit today into a
savings account that earns 4% in order to be able to withdraw $6,000 at the end of e/of
the next 5 years. He should use which present value concept?
a. present value of $1 for 5 periods
b. future value of an annuity due $1 for 5 periods
c. present value of an ordinary annuity of $1 for 5 periods
d. future value of $1 for 5 periods - answerc
He's looking for present value "money he needs to deposit today".
Ordinary annuity b/c he wants to withdraw at the end of e/period.
The Stinch Fertilizer Corporation wants to accumulate $8,000,000 for plant expansion.
The funds are needed on January 1, 2021. Stinch intends to make 5 equal annual
deposits in a fund that will earn interest at 7% compounded annually. The first deposit it
to be made January 1, 2016. Present value and future value facts are as follows:
What is the amount of the required annual deposit?
a. 1,300,813
b. 1,391,304
c. 1,951,220
d. 1,704,000 - answera
