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 $129,100.00 from his retirement account until he turns 94.00. After this final withdrawal, he wants $1.85 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.

Annual deposit = 13,346.55

Explanation:

Giving the following information:

Exactly one year after the day he turns 75.0 when he fully retires, he will begin to make annual withdrawals of $129,100.00 from his retirement account until he turns 94.00. After this final withdrawal, he wants $1.85 million remaining in his account.

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

Assume an 8.00% interest rate.

First, we need to calculate the amount of money needed at 65.

39 years*129,100 + 1,850,000 = $6,884,900

We need to calculate the value at 65:

PV = 6,884,900 / (1.08^10) = $3,189,040.85

We need to use the following formula:

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

A = annual deposit

Isolating A:

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

A = (3,189,040.85*0.08) / [ (1.08^39) - 1] = $13,346.55