Question

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. $

Answer 1

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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