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TIME VALUE OF MONEY
PRACTICE PROBLEMS |
The AMOUNT listed in Table 1 is invested in an
account paying the indicated interest rate, for the listed term and compounding
interval. The answer is the calculated
value at the end of the indicated term.
For example, the first line of the table is investing $1250
in an account earning 6% interest (compounded annually) for 1 year.
The last column in the table is investing $18,000 in an
account paying
11 15/16% interest (compounded daily) for 44 1/2 years.
Table 1
|
AMOUNT
|
RATE
|
COMPOUNDING
INTERVAL
|
YEARS
|
ANSWER
|
|
$1250
|
6.00%
|
Annual
|
1
|
$1325
|
|
$1800
|
7.10%
|
Annual
|
2
|
$2064.67
|
|
$2750
|
5 ¾%
|
Annual
|
9
|
$4548.37
|
|
$4225
|
7 ¼%
|
Semi Annually
|
6
|
$6477.41
|
|
$5665
|
6 ½%
|
Semi Annually
|
11
|
$11449.36
|
|
$6250
|
9 1/8%
|
Quarterly
|
22
|
$45491.54
|
|
$6995
|
11 5/8%
|
Quarterly
|
3
|
$9864.81
|
|
$7000
|
8 3/8%
|
Weekly
|
12
|
$19107.90
|
|
$7500
|
16 7/8%
|
Weekly
|
9 ¼
|
$35634.46
|
|
$8000
|
15 2/3%
|
Weekly
|
10 ½
|
$41345.70
|
|
$8250
|
7.7%
|
Monthly
|
11 ¾
|
$20329.50
|
|
$8666
|
8 1/8%
|
Monthly
|
7
|
$15275.35
|
|
$9125
|
6.33%
|
Monthly
|
18 ¼
|
$28899.12
|
|
$11250
|
7.225%
|
Daily
|
5.25
|
$16438.78
|
|
$22222
|
9.6175%
|
Daily
|
7 3/8
|
$45163.08
|
|
$5500
|
14.9138%
|
Daily
|
8 5/8
|
$19901.61
|
|
$6195
|
9 11/16%
|
Daily
|
9 3/4
|
$15929.11
|
|
$7175
|
10 13/16%
|
Daily
|
22.25
|
$79521.53
|
|
$18000
|
11 15/16%
|
Daily
|
44 1/2
|
$3647111.22
|
For table 2, the amount in the first column is the
amount that we will have in an account if invested at the given interest rate,
compounding period and number of years. Our task is to calculate what we
would need to deposit TODAY to have the stated amount.
Table 2
|
AMOUNT
|
RATE
|
COMPOUNDING
INTERVAL
|
YEARS
|
ANSWER
|
|
$1250
|
6.00%
|
Annual
|
1
|
$1179.25
|
|
$1800
|
7.10%
|
Annual
|
2
|
$1569.26
|
|
$2750
|
5 ¾%
|
Annual
|
9
|
$1662.68
|
|
$4225
|
7 ¼%
|
Semi Annually
|
6
|
$2755.83
|
|
$5665
|
6 ½%
|
Semi Annually
|
11
|
$2802.97
|
|
$6250
|
9 1/8%
|
Quarterly
|
22
|
$858.68
|
|
$6995
|
11 5/8%
|
Quarterly
|
3
|
$4960.06
|
|
$7000
|
8 3/8%
|
Weekly
|
12
|
$2564.38
|
|
$7500
|
16 7/8%
|
Weekly
|
9 ¼
|
$1578.53
|
|
$8000
|
15 2/3%
|
Weekly
|
10 ½
|
$1547.92
|
|
$8250
|
7.7%
|
Monthly
|
11 ¾
|
$3347.97
|
|
$8666
|
8 1/8%
|
Monthly
|
7
|
$4916.39
|
|
$9125
|
6.33%
|
Monthly
|
18 ¼
|
$2881.27
|
|
$11250
|
7.225%
|
Daily
|
5.25
|
$7699.02
|
|
$22222
|
9.6175%
|
Daily
|
7 3/8
|
$10934.09
|
|
$5500
|
14.9138%
|
Daily
|
8 5/8
|
$1519.98
|
|
$6195
|
9 11/16%
|
Daily
|
9 3/4
|
$2409.30
|
|
$7175
|
10 13/16%
|
Daily
|
22.25
|
$647.38
|
|
$18000
|
11 15/16%
|
Daily
|
44 1/2
|
$88.84
|
For table three, calculate the amount of the annuity if the
value in the "amount" column is invested under the given interest rate
and term. Remember, the cash flow frequency MUST equal the compounding
interval. [i.e., monthly deposits must be compounded monthly.]
Table 3
|
AMOUNT |
RATE |
YEARS |
ANSWER |
| $100 monthly |
7.75% |
5 1/2 |
$8,197 |
| $200 monthly |
8.125% |
8 |
$26,920 |
| $450 monthly |
9 1/4% |
9 1/4 |
$78,527 |
| $50 weekly |
6 5/8% |
10 1/4 |
$38,114 |
| $75 weekly |
7 2/3% |
5.7 |
$27,854 |
| $100 weekly |
6 3/4% |
12 3/4 |
$105,026 |
| $250 quarterly |
8 3/8% |
21 1/2 |
$59,008 |
| $500 quarterly |
9 1/2% |
7 |
$19,567 |
| $1000 quarterly |
10% |
10 |
$67,403 |
| $1000 semi-annually |
11.7% |
9 |
$30,470 |
| $1500 semi-annually |
12 11/16% |
17 3/4 |
$186,258 |
| $2500 semi-annually |
8 7/8% |
10.8 |
$87,575 |
| $2500 annually |
9.125% |
11.25 |
$45,776 |
| $5000 annually |
8.375% |
15 |
$139,789 |
| $7000 annually |
7.625 |
15 |
$184,608 |
| $1000 monthly |
6.1875% |
9 1/2 |
$154,634 |
| $250 weekly |
10 3/4% |
20 |
$914,937 |
| $6000 semi-annually |
11.5625% |
33 |
$4,133,654 |
| $12000 annually |
12.5% |
18.25 |
$727,768 |
Table 4 calculates the present value of the annuity under
the terms given.
Table 4
|
AMOUNT |
RATE |
YEARS |
ANSWER |
| $100 monthly |
7.75% |
5 1/2 |
$5,360 |
| $200 monthly |
8.125% |
8 |
$14,084 |
| $450 monthly |
9 1/4% |
9 1/4 |
$33,485 |
| $50 weekly |
6 5/8% |
10 1/4 |
$19,336 |
| $75 weekly |
7 2/3% |
5.7 |
$17,999 |
| $100 weekly |
6 3/4% |
12 3/4 |
$44,440 |
| $250 quarterly |
8 3/8% |
21 1/2 |
$9,931 |
| $500 quarterly |
9 1/2% |
7 |
$10,141 |
| $1000 quarterly |
10% |
10 |
$25,103 |
| $1000 semi-annually |
11.7% |
9 |
$10,951 |
| $1500 semi-annually |
12 11/16% |
17 3/4 |
$20,982 |
| $2500 semi-annually |
8 7/8% |
10.8 |
$34,283 |
| $2500 annually |
9.125% |
11.25 |
$17,139 |
| $5000 annually |
8.375% |
15 |
$41,835 |
| $7000 annually |
7.625 |
15 |
$61,313 |
| $1000 monthly |
6.1875% |
9 1/2 |
$86,035 |
| $250 weekly |
10 3/4% |
20 |
$106,813 |
| $6000 semi-annually |
11.5625% |
33 |
$101,242 |
| $12000 annually |
12.5% |
18.25 |
$84,812 |
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