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 $145,386.00 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 8.00% interest rate.

Answer format: Currency: Round to: 2 decimal places.

Answer 1

The value of the retirement account on 75th birthday is calculated using PV function in Excel :

rate = 8%

nper = 14 (14 annual withdrawals from 75th to 88th birthday)

pmt = 145386 (annual withdrawal)

fv = 0 (amount remaining in account after 14 years is zero)

type = 1 (each withdrawal is made at the beginning of the year)

PV is calculated to be $1,294,484.37

Present value = future value / (1 + interest rate)^{number of years}

There are 10 years between 65th and 75th birthday, when the retirement account grows at 8% per year

The value of the retirement account on 65th birthday is $1,294,484.37 / (1 + 8%)¹⁰ = $599,596.73

The annual contribution required is calculated using PMT function in Excel :

rate = 8%

nper = 40 (40 annual contributions from 26th 65th birthday)

pv = 0 (beginning amount in retirement account is zero)

fv =  599596.73 (required amount in retirement account on 65th birthday)

type = 1   (each withdrawal is made at the beginning of the year)

PMT is calculated to be $2,143.09

The annual contribution required is $2,143.09