Find the present value of an annuity with semiannual payments of $400 at 4.22%, compounded semiannually for 15 years.Round to the nearest cent.
A) $\quad P V = \$ 8,824.55$
B) $\quad P V = \$ 12,253.20$
C) $\quad P V = \$ 16,509.77$
D) $\quad P V = \$ 9,707.01$
E) $\quad P V = \$ 17,649.10$

Question

Find the present value of an annuity with semiannual payments of $400 at 4.22%, compounded semiannually for 15 years.Round to the nearest cent. 
A) $\quad P V = \$ 8,824.55$
B) $\quad P V = \$ 12,253.20$
C) $\quad P V = \$ 16,509.77$
D) $\quad P V = \$ 9,707.01$
E) $\quad P V = \$ 17,649.10$

Quizplus · Accepted Answer

We need to use the formula $PV = \dfrac{PMT}{r} \left(1-\dfrac{1}{(1+r)^n} \right)$ where $PMT$ is the semiannual payment amount, $r$ is the semiannual interest rate (which is $4.22\%/2 = 0.0211$), and $n$ is the total number of semiannual payments (which is $2\cdot 15 = 30$). Plugging in the values, we get $PV = \dfrac{400}{0.0211} \left(1-\dfrac{1}{(1+0.0211)^{30}} \right) \approx \$ 8,824.55$, rounded to the nearest cent. Thus, the best answer is A.

Find the Present Value of an Annuity with Semiannual Payments PV=$8,824.55\quad P V = \$ 8,824.55PV=$8,824.55

Find the Present Value of an Annuity with Semiannual Payments $\quad P V = \$ 8,824.55$