Question

Find the interest earned given the following:Amount needed: $14,500Time in years: 2 1/2Interest: 8%Compounded: quarterly

Answer 1

Given:

The amount needed is, A= $14,500

Time in years is t=2.5 years

Interest is 8%

To find the interest when it is calculated under compounded quarterly:

Using the formula,

$\begin{gathered} A=P(1+\frac{r}{4})^{4t} \\ 14500=P(1+\frac{0.08}{4})^{4(2.5)} \\ 14500=P(1+0.02)^{10} \\ 14500=P(1.02)^{10} \\ P=\frac{14500}{(1.02)^{10}} \\ P= 11,895.05 \end{gathered}$

Thus, the principal is $11,895.05

Then, the interest earned is,

Amount-Principal =$2,604.95

Thus, the interest is $2,604.95.