Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he...

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 begin to make annual withdrawals of \$108,596.00 from his retirement account until he turns 88.00. 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 10.00% interest rate.

Submit

To withdraw \$108,596.00 from his retirement account until he turns 88, he need to withdraw for a total of 13 years.

Present value of annuity is calculated as C*(1-(1+r)^-n)/r; where C is the annual cashflow, r is the discount rate and n is the number of years.

So, Value at 76th birthday should be 108596*(1-(1+10%)^-13)/10%= \$771396.07

For this he will make annual payments for 40 years until his 65th birthday. Let C be the payments.

Future value of annuity is calculated as C*(((1+r)^n)-1)/r; where C is the annual cashflow, r is the discount rate and n is the number of years.

((C*(1.1^40)-1)/10%).

From 65th birthday to 75th birthday, there will be no deposits or withdrawals. So,

((C*(1.1^40)-1)/10%)*(1.1^10)= 771396.07

C= \$671.96

The Contributuons should be \$671.96 each year.