4-14 a. Cash Stream A Cash Stream B
0 1 2 3 4 5 0 1 2 3 4 5
| | | | | | | | | | | |
PV = ? 100 400 400 400 300 PV = ? 300 400 400 400 100
With a financial calculator, simply enter the cash flows (be sure to enter CF0 = 0), enter
4-15 These problems can all be solved using a financial calculator by entering the known
values shown on the time lines and then pressing the I/YR button.
a. 0 1
| |
+700 -749
b. 0 1
| |
-700 +749
c. 0 10
| |
+85,000 -201,229
4-16 a. 0 12% 1 2 3 4 5
8%
8%
I = ?
I = ?
I = ?
| | | | | |
-500 FV = ?
d. 0 12 24 36 48 60
| | | | | |
-500 ?
4-17 a. 0 2 4 6 8 10
| | | | | |
PV = ? 500
10
06.1
1
1%
6%
3%
b. 0 4 8 12 16 20
| | | | | |
PV = ? 500
3%
1%
4-18 a. 0 1 2 3 9 10
| | | | | |
400 400 400 400 400
FVA10 = ?
c. The annuity in Part b earns more because some of the money is on deposit for a
4-19 a. Universal Bank: Effective rate = 7%.
With a financial calculator, you can use the interest rate conversion feature to obtain
the same answer. You would choose the Universal Bank.
b. If funds must be left on deposit until the end of the compounding period (1 year for
Universal and 1 quarter for Regional), and you think there is a high probability that
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
procedure as described in your calculator manual to get the entries for the
amortization table.
Repayment Remaining
Year Payment Interest of Principal Balance
1 $ 6,594.94 $2,500.00 $ 4,094.94 $20,905.06
*The last payment must be smaller to force the ending balance to zero.
b. Here the loan size is doubled, so the payments also double in size to $13,189.87: enter
c. The annual payment on a $50,000, 10-year loan at 10 percent interest would be
$8,137.27: enter N = 10, I/YR = 10, PV = -50000, and FV = 0, and then press the
4-21 a. 0 I=? 1 2 3 4 5
| | | | | |
-6 12 (in millions)
b. The calculation described in the quotation fails to take account of the compounding
effect. It can be demonstrated to be incorrect as follows:
4-23 0 1 2 3 4 30
| | | | | |
4-24 a. 0 1 2 3 4
| | | | |
b. (1) At this point, we have a 3-year, 7% annuity of $10,000 whose present value is
(Beginning balance)(1+I) – PMT = Ending balance
(2) Zero after the last withdrawal.
4-25 0 1 2 ?
| | | |
I = ?
7%
9%
4-26 0 1 2 3 4 5 6
| | | | | | |
With a financial calculator, get a “ballpark” estimate of the years by entering I/YR = 12,
Now find the FV of $1,250 for 5 years at 12%; N = 5, I/YR = 12, PV = 0, and PMT =
When the interest rate is doubled, the PV of the perpetuity is halved.
4-28 0 1 2 3 4
| | | | |
PV = ? 50 50 50 1,050
Discount rate: Effective rate on bank deposit:
8.24%
12%
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,
Pmt of Pmt of
Period Beg Bal Payment Interest Principal End Bal
You can also work the problem with a calculator having an amortization function. Find
4-30 First, find PMT by using a financial calculator: N = 5, I/YR = 15, PV = -1000000, and
FV = 0. Solve for PMT = $298,315.55. Then set up the amortization table:
Beginning Ending
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
Since the first payment is made today, we have a 5-period annuity due. The applicable
b. 1 10 years
0 1 2 3 4 5 40 quarters
| | | | | | |
The time line depicting the problem is shown above. Because the payments only
solved as an annuity problem. The problem can be solved in two steps:
(2) Then solve for PMT using the value solved in Step 1 as the FV of the
five-period annuity due.
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.
First, we must find the EAR = EFF% on the bank loan. Enter NOM% = 15, N =
P/YR = 12, and press EFF% to get EAR = 16.08%.
Nominal rate that should be quoted to customers:
3%
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
payments, we have this time line:
3. He now has $100,000 in an account which pays 8 percent, annual compounding. We
4. He wants to withdraw, or have payments of, $65,155.79 per year for 25 years, with
the first payment made at the beginning of the first retirement year. So, we have a
6. The $535,272.85 is the FV of a 10-year ordinary annuity. The payments will be
4-34 Information given:
The nominal time line is shown below, with a different payment each period and a FV of
a nominal $1 millon:
This is a growing annuity, with a nominal rate of 8% and an inflation rate of 3%. You
So the “real” time line in expressed in today’s purchasing power is:
8%
4.85437%