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An annuity pays $500 every six months for 5 years. The annual rate of interest is 8% convertible semiannually. Find each of the following: (a) The PV of the annuity six months (one period) before the first payment, (b) the PV of the annuity on the day of the first payment, (c) the FV of the annuity on the day of the last payment, (d) and the FV of the annuity six months after the last payment.

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Answer:

(a) The PV of the annuity six months (one period) before the first payment,

PV ordinary annuity = $500 x 8.1109 (PV annuity factor, 10 periods, 4%) = $4,055.45

(b) the PV of the annuity on the day of the first payment,

PV annuity due = $500 x 8.43533 (PV annuity due factor, 10 periods, 4%) = $4,217.67

(c) the FV of the annuity on the day of the last payment,

FV = $500 x 12.00611 (FV annuity factor, 4%, 10 periods) = $6,003.06

(d) and the FV of the annuity six months after the last payment.

FV = $6,003.06 x (1 + 4%) = $6,243.18

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