Question

# Future Value of an Annuity for Various Compounding Periods Find the future values of the following...

Future Value of an Annuity for Various Compounding Periods Find the future values of the following ordinary annuities. FV of \$200 each 6 months for 4 years at a nominal rate of 8%, compounded semiannually. Do not round intermediate calculations.

Round your answer to the nearest cent. \$ 2127.33 **incorrect** why is this wrong?

FV of \$100 each 3 months for 4 years at a nominal rate of 8%, compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent. \$

Solution :- (1)

Semiannual Rate = 8% / 2 = 4%

Semiannual Deposit = \$200

Total Semiannual Deposits = 4 * 2 = 8

Now the Future Value = Deposit * FVAF ( 4% , 8 )

= \$200 * [ ( 1 + 0.04 )8 - 1 ] / 0.04

= \$5,000 * 0.36857

= \$1,842.85

Solution :- (2)

Quarterly Rate = 8% / 4 = 2%

Quarterly Deposit = \$100

Total Semiannual Deposits = 4 * 4 = 16

Now the Future Value = Deposit * FVAF ( 2% , 16 )

= \$100 * [ ( 1 + 0.02 )16 - 1 ] / 0.02

= \$5,000 * 0.3728

= \$1,863.93

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