Question

Suppose Jenny borrows $5000 at an interest rate of 16% compounded each year.Assume that no payments are made on the loan.Follow the instructions below. Do not do any rounding.

Answer 1

Given:

Principal amount = $5000

Interest rate = 16%

Find-:

(a) Amount owed at the end of 1 year.

(b) Amount owed at the end of 1 year.

Sol:

The compound interest rate is:

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

Where,

$\begin{gathered} A=\text{ Amount after ''t'' time.} \\ \\ t=\text{ time in year.} \\ \\ r=\text{ Annual interest rate.} \\ \\ n=\text{ The number of times that interest is compounded per year.} \end{gathered}$

(a)

$\begin{gathered} t=1 \\ \\ n=1 \\ \\ r=\frac{16}{100} \\ \\ =0.16 \\ \\ p=5000 \end{gathered}$

Amount after one year.

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ =5000(1+\frac{0.16}{1})^{1\times1} \\ \\ =5000(1.16) \\ \\ =5800 \end{gathered}$

The amount after one year is $5800.

(b)

$\begin{gathered} P=5000 \\ \\ r=0.16 \\ \\ t=2 \\ \\ n=1 \end{gathered}$

So the amount after two years is:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ A=5000(1+\frac{0.16}{1})^{1\times2} \\ \\ A=5000(1.16)^2 \\ \\ A=5000\times1.3456 \\ \\ A=6728 \end{gathered}$

The amount after 2 years is $6728.