Wiley is currently 30 years old and wishes to save money to provide for his reti
ID: 2636493 • Letter: W
Question
Wiley is currently 30 years old and wishes to save money to provide for his retirement. Starting today, he will begin depositing the same fixed amount each year into a retirement savings account. His last deposit will be made when he retires at the age of 60. When he turns 62, he will withdraw $100,000 annually for each of the following 25 years (i.e. he will make 25 withdrawals in all). Assume that the retirement fund earns 12% annually over both the period that he is depositing money and the period he makes withdrawals. In order for Letterman to have sufficient funds in his account to fund his retirement, how much should he deposit annually?
The right answer is $2,851.27...i need a clear and complete working of how to get this answer.
Explanation / Answer
The PV of 25 withdrawals at year 62
= 100,000*PVIFA(12%,25)
= 100,000*(1-1.12^(-25))/.12
= 784,313.9112
The PV of 25 withdrawals at year 60
= 784,313.9112/1.12^2
= 625,250.2481
625,250.2481 is the FV of 31 deposits at year 6
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ps:31 deposits
first at the beginning of 30
second at the ending of 30
third at the ending of 31
...
31st at the ending of 60
---
625,250.2481 = A*(1 + FVIFA(12%,30))
A = 625,250.2481/(1 + FVIFA(12%,30))
= 625,250.2481/(1+(1.12^30-1)/.12)
= 2,580.13
It's almost the answer.
Thanks.
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