Question

If $14,000 is invested in an account for 15 years. Calculate the total interest earned at the end of 15years if the interest is:(a) 7% simple interest: $(b) 7% compounded annually: $(c) 7% compounded quarterly: $(d) 7% compounded monthly: $Round your answers to the nearest cent.

Answer 1

Hello!

Let's solve alternative (a):

For simple interest, we'll use the formula below:

$A=P(1+\frac{r}{100}\cdot t)$

Let's replace them with the values:

$\begin{gathered} A=14,000(1+0.07\cdot15) \\ A=14,000(1+1.05) \\ A=14,000\cdot2.05 \\ A=\ 28,700 \end{gathered}$

Solving alternative (b):

To compound interest, we'll modify the formula:

$A=P(1+\frac{r}{100})^t$

So, we'll have:

$\begin{gathered} A=14,000(1+0.07)^{15} \\ A=14,000(1.07)^{15} \\ A=14,000\cdot2.75903 \\ A=\ \text{ }38,626.42 \end{gathered}$

Solving alternative (c):

$\begin{gathered} A=P(1+\frac{r}{4})^{4t} \\ A=14,000(1+\frac{0.07}{4})^{4\cdot15} \\ A=14,000(1.0175)^{60} \\ A\cong \ \text{ }39,645.43 \end{gathered}$

Solving alternative (d):

$\begin{gathered} A=P(1+\frac{r}{12})^{12\cdot t} \\ A=14,000(1+\frac{0.07}{12})^{12\cdot15} \\ A\cong\ \text{ } 39,885.25 \end{gathered}$