Question

Erica is saving up money to buy a car. Erica puts $10,000.00 into an account which earns 4%interest, compounded monthly. How much will she have in the account after 3 years?

Answer 1

Since the money is applied in an account that is compounded, we need to use the following expression:

$A=P\cdot(1+\frac{r}{n})^{nt}$

Where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times the value gets compounded in a year and t is the elapsed time.

$\begin{gathered} A=10000\cdot(1+\frac{0.04}{12})^{3\cdot12} \\ A=10000\cdot(1+0.0033)^{36}_{} \\ A=10000\cdot(1.0033)^{36} \\ A=10000\cdot1.1273 \\ A=11272.72 \end{gathered}$

She will have $11272.72 in 3 years.