стр. 79 
A=
FV1FAi.n
In this problem, Sm = $1,000,000 and FVIFA8,20= 45.762. Therefore,
A = $lвЂ™oooвЂ™OOO $21,852.19
=
45.762
Loan Amortization. You have applied for a home mortgage of $75,000 to finance the purchase
61
.1
of a new home for 30 years. The bank requires a 14 percent interest rate. What will be the annual
payment?
SOLUTION
Solving P,, = A PVIFA,., for A yields:
Pn
A=
PVIFA,.n
Here P30= $75,000 and PVIFA14,H) 7.0027. Therefore,
=
A =  $75,000
= $10,710.16
7.0027
6 1 Loan Amortization. A commercial bank is willing to make you a loan of $10,000.The bank wants
.2
a 12 percent interest rate and requires five equal annual payments to repay both interest and
principal. What will be the dollar amount of the annual payment?
SOLUTION
Pn
A=
PVIFAj,n
Here P5= $10,000 and PVIFAIz,5= 3.6048. Therefore,
A =  $10вЂ™000  $2,774.08

3.6048
61
.3 Loan Amortization Schedule. Set up an amortization schedule for a $5,000 loan to be repaid in
equal installments at the end of each of the next 3 years. The interest rate is 15 percent.
169
TIME VALUE OF MONEY
CHAP. 61
SOLUTION
First, find the amount of equal installment by using the following formula:
PIl
A=
PVIFAi,,
In this problem P3 = $5,000 and PVIFA1s,J= 2.2832. Therefore,
A = $59000
= $2,189.91
2.2832
The amortization schedule is as follows:
Repayment Remaining
Year Payment Interest" of Principal Balance
$750
1 $3,560.09
$2,189.91 $1,439.91
$534.01
2 $2,189.91 $1,904.19
$1,655.90
$285.63
3 $2,189.82' $1,904.19'
Interest is computed by multiplying the loan balance at the beginning
of the year by the interest rate. Therefore, interest in year 1 is
$5,000(0.15) = $750; in year 2 interest is $3,560.09(0.15)= $534.01; etc.
Last payment is adjusted downward.
Not exact because of accumulated rounding errors.
61
.4 Annual Percentage Rate (APR). Suppose that a company borrows $20,000for 1year at a stated
rate of interest of 9 percent. What is the annual percentage rate (APR) if interest is paid to the
lender ( a ) annually? (b) semiannually? (c) quarterly?
SOLUTION
:)+
;
APR 1.0
= (1
In this problem r 9% = 0.09.
=
If interest is paid at the end of the year, rn = 1and
(a)
 1.0 = 1.09  1.0 = 0.09
APR = (1 +?)I = 9.0%
(b) If the interest is paid at the end of each 6month period, rn = 2 and
0.09
 1.0 = (1.045)2 1.0
APR = (1 + T )
= 1.092  1.0 = 0.092 = 9.2%
If interest is paid at the end of each quarter, rn = 4 and
(c)
0.09
7)= (1.0225)4  1.0
APR = (1 +  1.0
= 1.093  1.0 = 0.093 = 9.3%
More frequent payment of interest increases the effective annual cost paid by the company.
61
.5 Rate of Growth. If a firm's earnings increase from $3.00 per share to $4.02 over a 6year period,
what is the rate of growth?
[CHAP. 6
TIME VALUE OF MONEY
170
SOLUTION
Solving F, = P .FVIFi,, for FVIF yields:
FVIFj,, = 
Ffl
P
Here, P = $3.00 and F6 = $4.02. Therefore,
$4.02
FVIFi,6= = 1.340
$3.00
From Appendix A, an FVIF of 1.340 at 6 years is at i = 5%. The rate of growth of earnings is therefore
5 percent.
Annual Rate of Interest. You borrowed $20,000, to be repaid in 12 monthly installments of
6.16
$1,891.20. What is the annual interest rate?
SOLUTION
Solving P, = A .PVIFA,,, for PVIFA yields:
PVIFAi.n= 
pl
f
A
In this problem P12 $20,000 and A = $1,891.20. Therefore,
=
$20,000
стр. 79 