b. 0 1 2
| | | $500(1.06)2 = $561.80.
2-9 a. 0 1
b. 0 1 2
c. 0 1
d. 0 1 2
2-10 a. 0 1 2 3 4 5 6 7 8 9 10
b. 0 1 2 3 4 5 6 7 8 9 10
c. 0 1 2 3 4 5 6 7 8 9 10
| | | | | | | | | | |
a. 0 1 2 3 4 5 6 7 8 9 10
b. 0 1 2 3 4 5
| | | | | |
1. 0 1 2 3 4 5 6 7 8 9 10
2. 0 1 2 3 4 5
3. 0 1 2 3 4 5
2-15 a. 0 1 2 3 4 5 6 7 8 9 10
b. 0 1 2 3 4 5
c. 0 1 2 3 4 5
With a financial calculator, enter: N = 5, I/YR = 0, PMT = -400, and FV = 0. PV = $2,000.00.
d. 1. 0 1 2 3 4 5 6 7 8 9 10
| | | | | | | | | | |
400 400 400 400 400 400 400 400 400 400
PV = ?
With a financial calculator on BEG, enter: N = 10, I/YR = 10, PMT = -400, and FV = 0. PV = $2,703.61.
2. 0 1 2 3 4 5
| | | | | |
200 200 200 200 200
PV = ?
With a financial calculator on BEG, enter: N = 5, I/YR = 5, PMT = -200, and FV = 0. PV = $909.19.
3. 0 1 2 3 4 5
| | | | | |
400 400 400 400 400
PV = ?
With a financial calculator on BEG, enter: N = 5, I/YR = 0, PMT = -400, and FV = 0. PV = $2,000.00.
2-18 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
b. Set up an amortization table:
With a financial calculator, simply enter the cash flows (be sure to enter CF0 = 0), enter I/YR = 8, and press the NPV key to find NPV = PV = $1,251.25 for the first problem. Override I/YR = 8 with I/YR = 0 to find the next PV for Cash Stream A. Repeat for Cash Stream B to get NPV = PV = $1,300.32.
b. PVA = $100 + $400 + $400 + $400 + $300 = $1,600.
PVB = $300 + $400 + $400 + $400 + $100 = $1,600.
2-22 a. This can be done with a calculator by specifying an interest rate of 5% per period for 20 periods with 1 payment per period.
N = 10
2 = 20, I/YR = 10/2 = 5, PV = -10000, FV = 0. Solve for PMT = $802.43.
Beginning Payment of Ending
Period Balance Payment Interest Principal Balance
1 $10,000.00 $802.43 $500.00 $302.43 $9,697.57
2 9,697.57 802.43 484.88 317.55 9,380.02
$984.88
Because the mortgage balance declines with each payment, the portion of the payment that is applied to interest declines, while the portion of the payment that is applied to principal increases. The total payment remains constant over the life of the mortgage.
c. Jan must report interest of $984.88 on Schedule B for the first year. Her interest income will decline in each successive year for the reason explained in part b.
d. Interest is calculated on the beginning balance for each period, as this is the amount the lender has loaned and the borrower has borrowed. As the loan is amortized (paid off), the beginning balance, hence the interest charge, declines and the repayment of principal increases.
2-30 a. Using the information given in the problem, you can solve for the length of time required to reach $1 million.
Erika: I/YR = 6; PV = 30000; PMT = 5000; FV = -1000000; and then solve for N = 38.742182. Therefore, Erika will be 25 + 38.74 = 63.74 years old when she becomes a millionaire.
Kitty: I/YR = 20; PV = 30000; PMT = 5000; FV = -1000000; and then solve for N = 16.043713. Therefore, Kitty will be 25 + 16.04 = 41.04 years old when she becomes a millionaire.
b. Using the 16.0437 year target, you can solve for the required payment:
N = 16.0437; I/YR = 6; PV = 30000; FV = -1000000; then solve for PMT = $35,825.33.
If Erika wishes to reach the investment goal at the same time as Kitty, she will need to contribute $35,825.33 per year.
c. Erika is investing in a relatively safe fund, so there is a good chance that she will achieve her goal, albeit slowly. Kitty is investing in a very risky fund, so while she might do quite well and become a millionaire shortly, there is also a good chance that she will lose her entire investment. High expected returns in the market are almost always accompanied by a lot of risk. We couldn’t say whether Erika is rational or irrational, just that she seems to have less tolerance for risk than Kitty does.