Question

A loan of $39,000 is made at 6% interest, compounded annually. After how many years will the amount due reach $55,000 or more? (Use the calculatorprovided if necessary.)Write the smallest possiblewhole number answer.

Answer 1

Solution

Using the compound interest formula

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

Where

A= Amount due

P= Principal

r=rate per annum

n= number of years

$\begin{gathered} P(1+\frac{r}{100})^n\ge A \\ \\ 39000(1+0.06)^n\ge55000 \\ \\ 1.06^{^n}\ge1.410 \\ \\ n\ge\frac{\ln1.410}{\ln1.06} \\ \\ n\ge5.9 \end{gathered}$

The amount due will reach $55,000 or more after 6 years