Please assist with the following question: In the following ordinary annuity, th
ID: 2818028 • Letter: P
Question
Please assist with the following 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 9.2%. 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 $______________
Explanation / Answer
Joe:
Future value of annuity = Annuity * [ ( 1 + r)n - 1] / r
Future value of annuity = 5,000 * [ ( 1 + 0.092)30 - 1] / 0.092
Future value of annuity = 5,000 * 141.497578
Future value of annuity = $707,487.9
Joe will have $707,487.9 at age of 65.
Jill:
Number of periods = 30 * 52 = 1,560
Rate = 0.092 / 52 = 0.001769 or 0.1769%
Future value of annuity = 96.15 * [ ( 1 + 0.001769)1560 - 1] / 0.001769
Future value of annuity = 96.15 * 8,341.264192
Future value of annuity = $802,012.6
Jill will have $802,012.6 at age of 65.
Please note: Jill's amount will slightly change when calculated using a financial calculator due to rounding issues. using a financial calculator jill will accumulate an amount of $802,215.7
Keys to use in a financial calculator: 2nd I/Y 2, PMT 96.15, N 1560, I/Y 9.2, CPT FV