Question

Derek can deposit $16,687.00 on each birthday beginning with his 27.00th and ending with his 65.00th. What will the rate on the retirement account need to be for him to have $3,820,494.00 in it when he retires?

Answer format: Percentage Round to: 2 decimal places (Example: 9.24%, % sign required. Will accept decimal format rounded to 4 decimal places (ex: 0.0924))

Please show all steps or what to put into the financial calculator (not excel)

Answer 1

Annual Deposits = $ 16687, Deposits begin on the 27th birthday and end on the 65th birthday, Number of Tenures = (65-27) + 1 = 39, Target Future Value = $ 3820494

Let the annual rate be r%

Therefore, 16687 x (1+r)^(38) + 16687 x (1+r)^(37) +............+ 16687 = 3820494

16687 x [{(1+r)^(39)-1} / {(1+r)-1}] = 3820494

[{(1+r)^(39)-1} / {(1+r)-1}] = 3820494 / 16687 = $ 228.95

Using EXCEL's Goal Seek Function/hit and trial method/a financial calculator to solve the above equation we get:

r = 0.07832 or 7.832 % ~ 7.83 %