Appendix C
Present and Future Value Concepts
ANSWERS TO QUESTIONS
1. The time value of money is the idea that a dollar received today is worth more than a dollar
to be received at any later date because it can be invested today to earn interest over time.
2. Future value—The future value of a number of dollars is the amount that it will increase to
in the future at i interest rate for n periods. The future value is the principal plus
accumulated interest compounded each period.
Present value—The present value of a number of dollars, to be received at some specified
date in the future, is that amount discounted to the present at i interest rate for n periods. It
is the inverse of future value. In compound discounting, the interest is subtracted rather
than added as in compounding.
3. $10,000 x 2.5937 = $25,937 (a 259% increase).
4. $8,000 x .3855 = $3,084.
5. An annuity is a term that refers to equal periodic cash payments or receipts of an equal
amount each period for two or more periods. In contrast to a future value of $1, or a
present value of $1 (which involves a single contribution or amount), an annuity involves a
series of equal contributions for a series of equal periods. An annuity may refer to a future
value or a present value.
6. Table Values
Concept i = 5% n =4 i = 10%; n =7 i = 14%; n = 10
FV of $1 1.2155 1.9487 3.7072
PV of $1 .8227 .5132 .2697
FV of annuity of $1 4.3101 9.4872 19.3373
PV of annuity of $1 3.5460 4.8684 5.2161
7. $1,000 x 14.4866 = $14,487.
, Authors' Recommended Solution Time
(Time in minutes)
Mini-exercises Exercises Problems
No. Time No. Time No. Time
1 2 1 15 CP1 20
2 2 2 20 PA1 20
3 6 3 20 PB1 20
4 6 4 20
5 5
,ANSWERS TO MINI-EXERCISES
MC–1
$500,000 0.4632 = $231,600
MC–2
$15,000 6.1446 = $92,169
MC–3
$100,000 = $100,000
+ $100,000 0.9259 = 92,590
+ $ 30,000 9.8181 = 294,543
Total = $487,133
MC–4
$25,000 15.9374 = $398,435
$15,000 57.2750 = $859,125
It is much better to save $15,000 for 20 years.
, ANSWERS TO EXERCISES
EC–1
Req. 1
$6,000 x 2.5937 = $15,562
Req. 2
$15,562 – $6,000 = $9,562 (time value of money, or interest)
Req. 3
2007: $6,000 x 10% = $600 (interest)
2008: ($6,000 + $600) x 10% = $660 (interest)
EC–2
Req. 1
$80,000 x .7350 = $58,800
Req. 2
dr Cash—Savings account (+A) ...............................................
58,800
cr Cash—Checking account (-A) ......................................... 58,800
Req. 3
$80,000 – $58,800 = $21,200 (total interest)
Req. 4
December 31
(a) 2007 (b) 2008
dr Cash—Savings account (+A) ............. 4,704 5,080
cr Interest revenue (+R, +SE) ............ 4,704 5,080
Computations:
2007: $58,800 x 8% = $4,704.
2008: ($58,800 + $4,704) x 8% = $5,080.
Present and Future Value Concepts
ANSWERS TO QUESTIONS
1. The time value of money is the idea that a dollar received today is worth more than a dollar
to be received at any later date because it can be invested today to earn interest over time.
2. Future value—The future value of a number of dollars is the amount that it will increase to
in the future at i interest rate for n periods. The future value is the principal plus
accumulated interest compounded each period.
Present value—The present value of a number of dollars, to be received at some specified
date in the future, is that amount discounted to the present at i interest rate for n periods. It
is the inverse of future value. In compound discounting, the interest is subtracted rather
than added as in compounding.
3. $10,000 x 2.5937 = $25,937 (a 259% increase).
4. $8,000 x .3855 = $3,084.
5. An annuity is a term that refers to equal periodic cash payments or receipts of an equal
amount each period for two or more periods. In contrast to a future value of $1, or a
present value of $1 (which involves a single contribution or amount), an annuity involves a
series of equal contributions for a series of equal periods. An annuity may refer to a future
value or a present value.
6. Table Values
Concept i = 5% n =4 i = 10%; n =7 i = 14%; n = 10
FV of $1 1.2155 1.9487 3.7072
PV of $1 .8227 .5132 .2697
FV of annuity of $1 4.3101 9.4872 19.3373
PV of annuity of $1 3.5460 4.8684 5.2161
7. $1,000 x 14.4866 = $14,487.
, Authors' Recommended Solution Time
(Time in minutes)
Mini-exercises Exercises Problems
No. Time No. Time No. Time
1 2 1 15 CP1 20
2 2 2 20 PA1 20
3 6 3 20 PB1 20
4 6 4 20
5 5
,ANSWERS TO MINI-EXERCISES
MC–1
$500,000 0.4632 = $231,600
MC–2
$15,000 6.1446 = $92,169
MC–3
$100,000 = $100,000
+ $100,000 0.9259 = 92,590
+ $ 30,000 9.8181 = 294,543
Total = $487,133
MC–4
$25,000 15.9374 = $398,435
$15,000 57.2750 = $859,125
It is much better to save $15,000 for 20 years.
, ANSWERS TO EXERCISES
EC–1
Req. 1
$6,000 x 2.5937 = $15,562
Req. 2
$15,562 – $6,000 = $9,562 (time value of money, or interest)
Req. 3
2007: $6,000 x 10% = $600 (interest)
2008: ($6,000 + $600) x 10% = $660 (interest)
EC–2
Req. 1
$80,000 x .7350 = $58,800
Req. 2
dr Cash—Savings account (+A) ...............................................
58,800
cr Cash—Checking account (-A) ......................................... 58,800
Req. 3
$80,000 – $58,800 = $21,200 (total interest)
Req. 4
December 31
(a) 2007 (b) 2008
dr Cash—Savings account (+A) ............. 4,704 5,080
cr Interest revenue (+R, +SE) ............ 4,704 5,080
Computations:
2007: $58,800 x 8% = $4,704.
2008: ($58,800 + $4,704) x 8% = $5,080.
