Question

how much would $500 invested at 4% interest compounded monthly be worth after 5 years

Answer 1

The monthly interest rate is given by \(4\%/12\). The number of months it compounds is \(5\times 12\).

Answer 2

The normal compounding interest formula is: \[
p(t) = p_0(1+r)^t
\]But in this case, we make that adjustment: \[
p(t) = p_0\left(1+\frac rn\right)^{nt}
\]Where \(n=12\) because there are \(12\) months in a year.

Answer 3

And \(r=4\% = 0.04\), and \(p_0=\$500\).

Answer 4

They want \(t=5\), because 5 years.

Answer 5

\[
p(5) = 500\left(1+\frac{0.04}{12}\right)^{12(5)}
\]