Question

Calculate the amount of interest earned in 8 years on $16,000 deposited in the account paying 10% Annual interest compounded quarterly. Round to the nearest cent

Answer 1

Compound Interest

The final value of an investment P deposited at an interest rate r for t years is:

$FV=P\cdot(1+\frac{r}{m})^{t\cdot m}$

Where m is the number of times the investment earns interest in a year (compounding times per year).

In the problem, P = $16,000, r = 10% = 0.1, t = 8, and m = 4 (there are 4 quarters in a year).

Applying the formula:

$\begin{gathered} FV=\ 16,000\cdot(1+\frac{0.1}{4})^{4\cdot8} \\ \text{Operating:} \\ FV=\ 16,000\cdot(1.025)^{32} \\ FV=\ 16,000\cdot2.20376 \\ FV=\ 35,260.11 \end{gathered}$

Now we can calculate the amount of interest earned by subtracting:

I = FV - P

I = $35,260.11 - $16,000

I = $19,260.11