If $67,000 is invested in an annuity that earns an annual rate of 8.0%, compounded quarterly, what payments will it provide at the end of each quarter for the next 6.5 years? Round your answer to the nearest cent.
A)$2,823.46
B)$3,329.85
C)$2,490.47
D)$2,256.48
E)$2,084.31

Question

Quizplus · Accepted Answer

Using the formula for the future value of an annuity, $FV = P\left(\frac{(1+r)^n-1}{r}ight)$, where $P$ is the payment, $r$ is the interest rate per quarter, and $n$ is the total number of quarters, we can solve for $P$:
$$FV = P\left(\frac{(1+r)^n-1}{r}ight)$$
$$\frac{FV}{\frac{(1+r)^n-1}{r}} = P$$
Plugging in the values given, we get:
$$\frac{67,\!000}{\frac{(1+0.08/4)^{26}-1}{0.08/4}} \approx 3,\!329.85$$
Rounding to the nearest cent, we get $\boxed{	extbf{(B)}\ 3,\!329.85}$.

If $67,000 Is Invested in an Annuity That Earns an Annual