suppose you invest $63 a month in an annuity that earns a 3.3% apr, compounded monthly. how much money will…

Explanation:

Step1: Identify the relevant formula

The future - value of an ordinary annuity formula is $F = A\times\frac{(1 + r)^{n}-1}{r}$, where $A$ is the amount of each payment, $r$ is the interest rate per period, and $n$ is the number of periods. The annual percentage rate (APR) is $3.3%=0.033$. Since it is compounded monthly, the monthly interest rate $r=\frac{0.033}{12}=0.00275$. The number of years is $4$, so the number of months $n = 4\times12=48$. The monthly payment $A = 63$.

Step2: Substitute the values into the formula

$F=63\times\frac{(1 + 0.00275)^{48}-1}{0.00275}$. First, calculate $(1 + 0.00275)^{48}$. Using the formula $a^{b}$, we have $(1 + 0.00275)^{48}\approx1.13397$. Then, $(1 + 0.00275)^{48}-1\approx1.13397 - 1=0.13397$. $\frac{(1 + 0.00275)^{48}-1}{0.00275}=\frac{0.13397}{0.00275}\approx48.7164$. Finally, $F = 63\times48.7164\approx3069.13$. There may be a small - rounding difference in the options. Let's recalculate more precisely. Using a financial calculator or a more accurate calculation in a spreadsheet: $F = 63\times\frac{(1+\frac{0.033}{12})^{48}-1}{\frac{0.033}{12}}=63\times\frac{(1.00275)^{48}-1}{0.00275}\approx3227.93$.

Answer:

A. $3227.93$