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 $5000 each year. Joe and Jill both will make IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.8%. Joe deposits $5000 once each year, while Jill has $96.15 (which is 5000/52) withheld from her weekly paycheck and deposited automatically. How much will each have at age 65? (Round your answer to the nearest cent.)

Joe $

Jill $

Answer 1

Joe's Accumulation:

Deposit Tenure = 30 years, Deposit Amount = $ 5000, Yield = 9.8 %

Total Deposit at age 65 = 5000 x (1.098)^(29) + 5000 x (1.098)^(28) + .............+ 5000 x (1.098) + 5000 = $ 791953.8

Jill's Accumulation:

Deposit Tenure = 30 years = 52 x 30 = 1560 weeks, Deposit Amount = $ 96.15, Yield = 9.8 % or 0.8167 % per week

Total Deposit at age 65 = 96.15 x (1.008167)^(1559) + 96.15 x (1.008167)^(1558) + 96.15 x (1.008167)^(1557) + ........+ 96.15 x (1.008167) + 96.15 = $ 3815492723.51