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 9.6%. 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		$

In the tollowing ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period An individuetiement account, or IRA, ears tax-defered interest and allows the owner to invest up to $5000 each year. Joe a both will nake IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.6%. Ine deposits $500 once each year, while lill has $96.15 which is 5000 52 withheld fra herwaekly a check and deposited automatically. Ho much Leach have at gean un r answer to the nearest cent.) Joe Jill Need Help? Read ItWatchI Talk to a Tutor

Answer 1

Answer:

For Joe

Payment of annuity P =$5000/year

Interest rate r=9.6% per annum

Time for annuity n = 30 years

So Amount joe will get at 65 years=P*{(1+r)^n-1}/r=5000*{(1+9.6%)^30-1)/9.6%=$762,649.83

For Jill

Payment of annuity P =$96.15/week

Interest rate =9.6% per annum

So weekly interest rate r=9.6%/52=0.185%

Time for annuity n = 30*52= 1560 weeks

So Amount jill will get at 65 years=P*{(1+r)^n-1}/r=96.15*{(1+0.185%)^1560-1)/0.185%=$873,248.17