# A 7-year annuity of fourteen $10,600 semiannual payments will begin 9 years from now, with the... ## Question: A 7-year annuity of fourteen$10,600 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. If the discount rate is 9% compounded monthly, what is the value of this annuity five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

If the discount rate is 9% compounded monthly, what is the value three years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

If the discount rate is 9% compounded monthly, what is the current value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

## Present Value of Annuity:

An annuity is a stream of equal payments, occurring at a regular time interval. The present value of an annuity is the sum of the present value of each payment in an annuity.

We can use the following formula to compute the present value of an annuity with periodic payments {eq}M {/eq} for {eq}T{/eq} periods, given periodic return {eq}r{/eq}:

• {eq}\displaystyle \frac{M(1 - (1 + r)^{-T})}{r} {/eq}, when the first payment is expected in one period.

Given a 9% discount rate compounded monthly, we first compute the effective semiannual discount rate, which is:

• {eq}(1 + 9\%/12)^6 - 1 = 4.585\% {/eq}

Applying this formula, we can first compute the value of the annuity at the end of 9 years:

• {eq}\displaystyle \frac{10,600(1 - (1 + 4.585\%)^{-14})}{4.585\%} = 107,764.43 {/eq}

To find the value 5 years from now, we need to discount the value 9 years from now 4 years back, i.e.,

• {eq}\displaystyle \frac{107,764.43}{(1 + 4.585\%)^{8}} = 75,285.76 {/eq}

To find the value 3 years from now, we need to discount the value 9 years from now 6 years back, i.e.,

• {eq}\displaystyle \frac{107,764.43}{(1 + 4.585\%)^{12}} = 62,926.20 {/eq}

To find the value now, we need to discount the value 9 years from now 9 years back, i.e.,

• {eq}\displaystyle \frac{107,764.43}{(1 + 4.585\%)^{18}} = 48,084.99 {/eq}