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 | $ |
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
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