Answers and Solutions: 4 -11
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c. 0 10
| |
+85,000 -201,229
With a financial calculator, enter N = 10, PV = 85,000, PMT = 0, and FV = -201,229.
+9,000 -2,684.80 -2,684.80 -2,684.80 -2,684.80 -2,684.80
With a financial calculator, enter N = 5, PV = 9,000, PMT = -2,684.8, and FV = 0.
4-16 a. 0 12% 1 2 3 4 5
| | | | | |
-500 FV = ?
then press FV to obtain FV = $895.42.
c. 0 4 8 12 16 20
| | | | | |
With a financial calculator, enter N = 60, I/YR = 1, PV = -500, and PMT = 0, and
then press FV to obtain FV = $908.35.
I = ?
3%
4-17 a. 0 2 4 6 8 10
| | | | | |
PV = ? 500
With a financial calculator, enter N = 10, I/YR = 6, PMT = 0, and FV = –500. Then
press the PV key to find PV = $279.20.
Alternatively,
PV = FVn
mn
m
i
1
1
= $500
)5(2
2
12.0
1
1
= $500
10
06.1
1
= $500(PVIF6%, 10) = $500(0.5584) = $279.20.
b. 0 4 8 12 16 20
| | | | | |
PV = ? 500
With a financial calculator, enter N = 20, I/YR = 3, PMT = 0, and FV = -500. Then
6%
3%
4-18 a. 0 1 2 3 9 10
| | | | | |
FV = $5,272.32.
b. Now the number of periods is calculated as N = 5 x 4 = 20, I/YR = 12/4 = 3, PV =
c. The annuity in Part b earns more because some of the money is on deposit for a
longer period of time and thus earns more interest. Also, because compounding is
4-19 a. Universal Bank: Effective rate = 7%.
Regional Bank:
Effective rate =
4
4
06.0
1
– 1.0 = (1.015)4 – 1.0
you will make a withdrawal during the year, the Regional account might be
preferable. For example, if the withdrawal is made after 10 months, you would earn
nothing on the Universal account but (1.015)3 – 1.0 = 4.57% on the Regional account.
Ten or more years ago, most banks and S&Ls were set up as described above, but
6%
4-20 a. With a financial calculator, enter N = 5, I/YR = 10, PV = -25000, and FV = 0, and
then press the PMT key to get PMT = $6,594.94. Then go through the amortization
Year Payment Interest of Principal Balance
1 $ 6,594.94 $2,500.00 $ 4,094.94 $20,905.06
$32,974.69 $7,974.69 $25,000.00
*The last payment must be smaller to force the ending balance to zero.
$8,137.27: enter N = 10, I/YR = 10, PV = -50000, and FV = 0, and then press the
PMT key to get PMT = $8,137.27. Because the payments are spread out over a
4-21 a. 0 I=? 1 2 3 4 5
| | | | | |
effect. It can be demonstrated to be incorrect as follows:
$6,000,000(1.20)5 = $6,000,000(2.4883) = $14,929,800,
Answers and Solutions: 4 -15
4-22 0 1 2 3 4 5 6 7 8 9 10
7.18%.
4-23 0 1 2 3 4 30
I/YR = 9%.
4-24 a. 0 1 2 3 4
| | | | |
$26,243.16: N = 3, I/YR = 7, PMT = -10000, and FV = 0. Then press PV to get
PV = $26,243.16. You can also think of the problem as follows:
4-25 0 1 2 ?
| | | |
I = ?
I = ?
7%
9%
or in part.
4-26 0 1 2 3 4 5 6
| | | | | | |
PV = 0, PMT = -1250, and FV = 10000, and then pressing the N key to find N = 5.94
years. This answer assumes that a payment of $1,250 will be made 94/100th of the way
$7,941.06(1.12) = $8,893.99. Thus, you will have to make a payment of $10,000 –
$8,893.99 = $1,106.01 at Year 6, so the answer is: it will take 6 years, and $1,106.01 is
4-27 PV = $100/0.07 = $1,428.57. PV = $100/0.14 = $714.29.
4-28 0 1 2 3 4
| | | | |
= 50, and FV = 1000, then press the PV key to get PV = $893.26
8.24%
12%
or in part.
4-29 This can be done with a calculator by specifying an interest rate of 5% per period for 20
periods with 1 payment per period to get the payment each 6 months: N = 10 2 = 20,
Period Beg Bal Payment Interest Principal End Bal
1 $10,000.00 $802.43 $500.00 $302.43 $9,697.57
the interest in each 6-month period, sum them, and you have the answer. Even simpler,
with some calculators such as the HP-10B, allow you to find the interest paid during a
4-30 First, find PMT by using a financial calculator: N = 5, I/YR = 15, PV = -1000000, and
Year Balance Payment Interest Principal Balance
4-31 a. Begin with a time line:
6-mos. 0 1 2 3 4 5 6 8 10 12 14 16 18 20
Years 0 6% 1 2 3 4 5 6 7 8 9 10
the value at the 5th 6-month period, which is t = 2.5. Now we must compound out to t
= 10, or for 7.5 years at an EAR of 12.36%, or 15 semiannual periods at 6%.
$597.53 20 – 5 = 15 periods @ 6% $1,432.02,
b. 1 10 years
0 1 2 3 4 5 40 quarters
| | | | | | |
PMT PMT PMT PMT PMT FV = 1,432.02
(2) Then solve for PMT using the value solved in Step 1 as the FV of the five–
period annuity due.
Step 1: Input the following into your calculator: N = 35, I/YR = 3, PMT = 0, FV
3%
Answers and Solutions: 4 -19
4-32 Here we want to have the same effective annual rate on the credit extended as on the
bank loan that will be used to finance the credit extension.
next quarter. Therefore, enter P/YR = 4, EFF% = EAR = 16.08%, and press NOM% to
find the nominal rate of 15.19 percent.
quoted to the customers.
1.1608 = (1 + INOM/4)4
1.0380 = 1 + INOM/4
4-33 Information given:
1. Will save for 10 years, then receive payments for 25 years.
2. Wants payments of $40,000 per year in today’s dollars for first payment only. Real
income will decline. Inflation will be 5 percent. Therefore, to find the inflated fixed
$65,155.79.
3. He now has $100,000 in an account which pays 8 percent, annual compounding. We
need to find the FV of the $100,000 after 10 years. Enter N = 10, I/YR = 8, PV = –
get PV = $751,165.35. This amount must be on hand to make the 25 payments.
5. Since the original $100,000, which grows to $215,892.50, will be available, we must
save enough to accumulate $751,165.35 – $215,892.50 = $535,272.85.