Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 75.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 75.0 when he fully retires, he will wants to have $2,934,725.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 4.00% interest rate.

Answer 1

Derel wants to have $2934,725 one year after he turns 75,i.e., on age 76 he wants to have $2934,725

Calculating the Present Value at age 65 from age 76:-

Present Value =Accumulated value at age 76/(1+r)^n

where, r= Interest rate = 4%

n = no of years = 11 years

Present Value = $2934,725/(1+0.04)^11

= $2934,725/1.53945405632

= $1906,341.40

Now, Derek will make annual contribution to his account from age 26 to age 65 such that he can have $1906,341.40 at age 65 in his account:-

Where, C= Periodic Payments

r = Periodic Interest rate = 4%

n= no of periods = 39 years

C = $20,061.36

So, the contribution should be $20,061.36

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