(A) A man deposits $2,000 in an IRA on his 21st birthday and on each subsequent

Question

(A) A man deposits $2,000 in an IRA on his 21st birthday and on each subsequent birthday up to, and including his 29th (nine deposits in all). The amount earns 8% compounded annually. If he leaves the money in the account without making any more deposits, how much will he have on his 65th birthday, assuming the account continues to earn the same rate of interest? (B) How much would be in the account (to the nearest dollar) on his 65th birthday if he had started the deposits on his 30th birthday and continued making deposits on each birthday until (and including) his 65th birthday?

Explanation / Answer

First: Use Future Value of Ordinary Annuity to calculate the amount he'll have after 10 payments.
FVoa = PMT [((1 + i)^n - 1) / i]
i = 0.08 , n=10
FVoa = 2,000 ((1.08^10 - 1)/0.08)
= 2,000(14.486562)
= 28,973.12 <<amt in account after 10th pmt on 30th b-day.

A.) periodic rate "i"= .075annualrate / 2periods per year = 0.0375 for semi-annual "i"; and n = 2periods per year * 35yrs to retirement = 70

FV = PV(1 + i)^n
where PV is the amount in the account on his 30th bday.
FV = 28,973.12 (1.00375^70)
= $381,208.56 <<amount he'll have at age 65.

B.) for total interest earned, use the final (future) value (in A) and subtract all the payments HE made ($2,000 * 10)
381,208.56 - 20,000 = $361,208.55 total interest earned over the life of the investment(s)

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