Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 71.00. 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 71.0 when he fully retires, he will begin to make annual withdrawals of $167,806.00 from his retirement account until he turns 87.00. After this final withdrawal, he wants $1.30 million remaining in his 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 8.00% interest rate.

Answer 1

Solution:-

First, Calculation of Amount Derek will need on his 71^th birthday:

=16 years (71-87 years) X $167.806 + $1.3 million

=$3,984,896

Value of $3,984,896 on his 65^th birthday i.e. years before

PV= 3,984,896/(1.08^6)= $2,511,160

He will make contributions to his retirement account from his 26th birthday to his 65th birthday.

Ie 39 years at 8.00% interest rate.

Thus using the annuity formula, find annual contributions to be made.

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

Thus, A= (FV*i)/{[(1+i)^n]-1}

Ie. (2,511,160*0.08)/[(1.08^39)-1]=

Ie.$10,509.5 is the amount of annual contribution.