Which of the following will have the highest value after 20 years, assuming the same annual interest rate of 10%?
A. |
$170,000 deposited after 5 years |
|
B. |
$110,000 deposited now |
|
C. |
$20,000 deposits per year for 8 years, starting from now |
|
D. |
10 yearly deposits from now that grows at 12% per year, with $10,000 as the first deposit (i.e., 10,000 now, 11,200 in a year, 12,544 in 2 years, etc.) |
C. |
$20,000 deposits per year for 8 years, starting from now has the highest value after 20 years |
Working:
A. | Value after 20 years | = | 170000*(1+0.10)^15 | = | $ 7,10,132.19 | ||
B. | Value after 20 years | = | 110000*(1+0.10)^20 | = | $ 7,40,024.99 | ||
C. | |||||||
# 1 | |||||||
Value after 7 years from now | = | Annuity*Future Value of annuity of 1 | |||||
= | $ 20,000.00 | * | 12.57947691 | ||||
= | $ 2,51,589.54 | ||||||
Future value of annuity of 1 | = | ((((1+i)^n)-1)/i)*(1+i) | |||||
= | ((((1+0.10)^8)-1)/0.10)*(1+0.10) | ||||||
= | 12.57948 | ||||||
# 2 | |||||||
Value after 20 years | = | $ 2,51,589.54 | *(1+0.10)^13 | ||||
= | $ 8,68,555.32 | ||||||
D. | |||||||
Deposit number | Year | Cash flows | Future Value of 1 | Future Value of cash flows | |||
a | b | c=1.10^(20-a) | d=b*c | ||||
1 | 0 | $ 10,000.00 | 6.727499949 | $ 67,275.00 | |||
2 | 1 | $ 11,200.00 | 6.115909045 | $ 68,498.18 | |||
3 | 2 | $ 12,544.00 | 5.559917313 | $ 69,743.60 | |||
4 | 3 | $ 14,049.28 | 5.054470285 | $ 71,011.67 | |||
5 | 4 | $ 15,735.19 | 4.594972986 | $ 72,302.79 | |||
6 | 5 | $ 17,623.42 | 4.177248169 | $ 73,617.39 | |||
7 | 6 | $ 19,738.23 | 3.797498336 | $ 74,955.88 | |||
8 | 7 | $ 22,106.81 | 3.452271214 | $ 76,318.72 | |||
9 | 8 | $ 24,759.63 | 3.138428377 | $ 77,706.33 | |||
10 | 9 | $ 27,730.79 | 2.853116706 | $ 79,119.17 | |||
Total | $ 7,30,548.73 |
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