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 begin to make annual withdrawals of $185,307.00 from his retirement account until he turns 95.00. 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 4.00% interest rate. Currency: Round to: 2 decimal places.

Answer 1

Step-1:

First we have to calculate present value of annual withdrawls at the age of 75

From 75 to 95 number of periods 20

Using excel PV Function

=PV(4%, 20,185307,0)

Present value = 2,518,382.60

Step-2:

Again we have to calculate present value at age 65

From 65 to 75 number of periods 10(n)

Present value = future value / (1+r)^n

= 2518382.60 / (1+4%)^10

= 1,701,329.05

Step - 3:

Now we have to calculate annual contributions using above amount as future value

26 to 65 number of deposits 40 (including 26)

Using excel PMT Function

=PMT(4%,40,0,1701329.05)

So annual contributions = $17,903.92

(In case of any further explanation please comment)