In the following ordinary annuity, the interest is compounded with each payment,

Question

In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

An individual retirement account, or IRA, earns tax-deferred interest and allows the owner to invest up to $5,000 each year. Jack and Jill both make IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.5%. Jack deposits $5000 once each year, while Jill has $96.15 (which is 5,000/52) withheld from your weekly paycheck and deposited automatically. How much will each have at the age of 65?

Explanation / Answer

JacK:

amout at the age of 65 = 5000*(F/A, 9.5%, 30) = 5000*149.6875 = $748,438

Jill:

weekly interest = 9.5/52 = 0.18269 %

number of periods, n = weeks in 30 years = 52*30 = 1560

amout at the age of 65 = 96.15*(F/A, 0.18269 %, 1560) = 96.15*8890.6174 = $854,867

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