This is actuarial science. Please answer asap. thank you! Problem 6 - Equations of Value A...
This is actuarial science. Please answer asap. thank you!
Problem 6 - Equations of Value
A deposit X is to be made today and a second deposit, which is
twice the first, is to be made 6 years from now, to provide for
withdrawals of $4000 two years from now and $9500 9 years from
now.
At an effective annual interest rate of 3%, calculate the size of
the first deposit.
Homework Answers
| Years | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Deposits | X | 2X | ||||||||
| Withdrawals | $4,000 | $9,500 | ||||||||
| Present value of Withdrawals | 3770 | |||||||||
| (4000/(1.03)^2) | ||||||||||
| 7281 | ||||||||||
| (9500/(1.03)^9) | ||||||||||
| Total present value of withdrawals | $11,051 | |||||||||
| Present value of Deposit "2X" | 1.6749685 X | |||||||||
| (2X/(1.03)^6*2) | ||||||||||
| Total present value of deposits | 2.6749685 X | (X +1.6749685 X) | ||||||||
| Hence, | =2.6749685 X = 11,051 | |||||||||
| so, X = 11,051/2.6749685 | ||||||||||
| X = $ 4,131 | ||||||||||
| Hence, size of the first deposit = | $4,131 | |||||||||
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This is actuarial science. Please answer asap. thank
you!
Problem 6 - Equations of Value
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