Question

If Derek plans to deposit $13,117.00 into his retirement account on each birthday beginning with his 26th and the account earns 4.00%, how long will it take him to accumulate $3,817,949.00?

Answer format: Number: Round to: 2 decimal places.

Derek decides that he needs $157,131.00 per year in retirement to cover his living expenses. Therefore, he wants to withdraw $157131.0 on each birthday from his 66th to his 85.00th. How much will he need in his retirement account on his 65th birthday? Assume a interest rate of 6.00%.

Answer format: Currency: Round to: 2 decimal places.

Answer 1

Answer-Part-1

Deposite amount is $13117 in the begin of the year(A)

Required Future value = $3817949

t= ???

r= 4% or 0.04

Future value of an annuity Due =

=>3817949 =

=>

=>

=>

=>t * 0.01703333929 = 1.08618002402 [ log 1.04 =0.01703333929 and log 12.19495=1.08618002402 ]

=>t = 63.76788518 or 63.77 years

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Answer-Part-2

As we know

PV of an annuity =

Hence

Amount needed in retirement account on 65th birthday = Annual withdrawals*

=>Amount needed in retirement account on 65th birthday=

=>Amount needed in retirement account on 65th birthday = $1802280.19

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