Question

If you deposit $12,500 in an account that pays 4.5% interest quarterly, what is the balance after 8 years? How much did the account earn in interest?

Answer 1

In order to determine the balance of the account, use the following formula for the amount of money obtained after t years, basen on a compound interest:

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

where,

P: principal = $12,500

A: amount earnt after t years = ?

r: interest rate in decimal form = 0.045 (4.5%)

n: times at year for the compund interes = 4 (quaterly)

Replace the previous values of the parameters into the formula for A and simplify:

$\begin{gathered} A=12,500(1+\frac{0.045}{4})^{4\cdot8} \\ A=12,500(1+0.01125)^{32} \\ A=12,500(1.01125)^{32} \\ A=12,500(1.430451402) \\ A\approx17,880.64 \end{gathered}$

Hence, the balance after 8 years is approximately $17,880.64 in the account.

The interest earnt by the account is given by the difference between the previous result and the principal invesment:

I = $17,880.64 - $12,500 = $5,380.64

Hence, the interest earnt is $5,380.64