Question

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

Find the amount of time needed in years for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.)

$4500 yearly at 7% to accumulate $100,000.

2.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 9.3%. 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		$

3. Calculate the present value of the annuity. (Round your answer to the nearest cent.)

$13,000 annually at 5% for 10 years.

Answer 1

1.

Time needed in years for the sinking fund to reach the given accumulated amount can be calculated using the nper function in excel

=NPER(0.07,-4500,0,100000)

=13.87 years

2.

Future value needs to calculated for Joe and Jill, it can be achieved using the excel function FV

Jill =FV(0.093,30,-5000,,) = $720,862.28

Joe =FV(0.093/52,1560,-96.15,,) = $819,348.90

1560 are the number of months derived by multiplying 30 years with 52 weeks.

3.

The present value of annuity can be calculated using the PV function:

=PV(0.05,10,-13000,,)

=$100,382.55