Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 73.00. 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 73.0 when he fully retires, he will wants to have $3,310,550.00 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 5.00% interest rate.

Answer 1

Solution:-

Calculation of Amount Derek will need on his 73^th birthday: $3,310,550.00

Value of $3,310,550.00 on his 65^th birthday i.e. years before

PV= 3,310,550/(1.05^8)= $2240710.55

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

Ie 39 years at 5.00% 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. (2240710*0.05)/[(1.05^39)-1]= $19639

Ie.$ $19639 is the amount of annual contribution.