Find the future values of the following ordinary annuities F

Find the future values of the following ordinary annuities:

FV of $800 paid each 6 months for 5 years at a nominal rate of 9% compounded semiannually. Round your answer to the nearest cent.

$ FV of $400 paid each 3 months for 5 years at a nominal rate of 9% compounded quarterly. Round your answer to the nearest cent.

$ These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. Why does this occur?

Solution

a.

FV = $9,830.57

Using financial calculator BA II Plus - Input details:

#

I/Y = Rate or yield = 9/2 =

4.50

PMT = Payment =

-$800.00

N = Total number of compounding period = 5 x 2 =

10

PV = Present Value =

$0.00

CPT > FV = Future Value =

$9,830.57

b.

FV = $9,964.61

Using financial calculator BA II Plus - Input details:

#

I/Y = Rate or yield = 9/4 =

2.25

PMT = Payment =

-$400.00

N = Total number of compounding period = 5 x 4 =

20

PV = Present Value =

$0.00

CPT > FV = Future Value =

$9,964.61

FV (b) has quarterly compounding and FV(a) has semiannual compounding because payment happens every 3 months in FV (b).

FV (b) is greater than FV (a) because the compounding period is higher for FV (b). As we increase compounding the return increases on years basis and keeps earning interest on interest for the life of the investment.