Question

Shen took out a loan for 7600 that charges an annual interest rate of 8.2%, compounded monthly. Answer each part

Answer 1

Step 1

Given;

$\begin{gathered} P=7600 \\ r=\frac{8.2}{100}=0.082 \\ t=1 \end{gathered}$

Step 2

A) she will owe

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=7600(1+\frac{0.082}{12})^{12\times1} \\ A=\text{ \ }8247.16 \end{gathered}$

B) The effective annual rate is given as;

$\begin{gathered} R=(1+\frac{i}{n})^n-1 \\ R=[(1+\frac{0.082}{12})^{12}-1]\times100 \\ R=0.08515\times100=8.515\text{\%} \\ R\approx8.52\text{\%} \end{gathered}$