Question

Scheduled payments of $477, $1137, and $449 are due in one-and-a-half years, four years, and five-and-a-half years respectively. What is the equivalent single replacement payment two-and-a-half years from now if interest is 9% compounded semi-annually? The equivalent single replacement payment is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

If the interest is 9% compounded semi-annually, then the effective interest per period is 4.5% = 0.045, in decimal notation.

First let us find the present value of all the payments.

$477 is due one and a half years, i.e. 3 periods from now, so the present value is given by

$\small P_1(1.045)^3=477\Rightarrow P_1 = 417.993480$

$1137 is due four years, i.e. 8 periods from now, so the present value is given by

$\small P_2(1.045)^8=1137\Rightarrow P_2 =799.521489$

$449 is due in five and a half years, i.e. 11 periods, so the present value is given by

$\small P_3(1.045)^{11}=449\Rightarrow P_3 =276.673234$

Thus, adding P1,P2,P3 we get the total present value of all the payments as

$\small P=417.993480+799.521489+276.673234=1494.188203$

Thus, the answer is given by the amount this present value will become after 2 and a half years, i.e. 5 periods, so

$\small A=1494.188203(1.045)^5=1862.03035$

Thus, the equivalent single replacement payment is $ 1862.03