# Present Value of an Annuity - Compounding and Payment Periods

A 5-year annuity of ten $5,300 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now.

1. If the discount rate is 12 percent compounded monthly, what is the value of this annuity five years from now?

2. If the discount rate is 12 percent compounded monthly, what is the value three years from now?

If the discount rate is 12 percent compounded monthly, what is the current value of the annuity?

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#### Solution Preview

A 5-year annuity of ten $5,300 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now.

1. If the discount rate is 12 percent compounded monthly, what is the value of this annuity five years from now?

This is an ordinary annuity starting 9 years from now. Its value at inception will be:

PV $38,729.05 This is the value 9 years from now

FV $- This is the remaining value after the last payment is made

PMT $(5,300.00) This is the amount of each semiannual payment

NPER 10.00 This is the number of semiannual payments

RATE 6.15% This is the discount rate ...

#### Solution Summary

This solution illustrates how to convert a monthly rate to a semiannual effective rate and how to find the present value of an annuity at different intervals where the compounding periods differ from the payment periods.