Question

Suppose Latoya borrows$4000.00 at an interest rate of 18% compounded each year.Assume that no payments are made on the loan.Find the amount owed at the end of 1 year.Find the amount owed at the end of 2 years.

Answer 1

`\begin{gathered} A=\text{ \$4,720 at the end of 1 year} \\ A=\text{ \$5,570 at the end of 2 year} \end{gathered}`

Explanation:

The compound interest is represented by the following equation:

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ where, \\ P=\text{ principal borrowed} \\ r=\text{ rate} \\ n=\text{ number of times compounded per time ''t''} \\ t=\text{ time in years} \end{gathered}`

Therefore, if Latoya borrows $4000 at an interest rate of 18% compounded each year;

`\begin{gathered} A=4000(1+(0.18)/(1))^1 \\ A=\text{ \$4,720 at the end of 1 year} \end{gathered}`

Now, at the end of 2 years:

`\begin{gathered} A=4000(1+(0.18)/(2))^2 \\ A=\text{ \$5,569.6 at the end of 2 year} \end{gathered}`