Question

If a business borrows $100,000 and repays $129,750 in four years, what is the simple annual interest rate?

Answer 1

Suppose that the debt was completely paid after 4 years; then, 4 years of interest have passed.

The initial debt is $100000, and the interest is applied each year.

Year 1: 100000(1+r)

Where r is the interest rate.

Year 2: (100000(1+r))(1+r)=100000(1+r)^2

And so on.

Thus, after four years, the debt is:

`\begin{gathered} Debt=100000(1+r)^4 \\ \Rightarrow129750=100000(1+r)^4 \end{gathered}`

Solving for r

`\begin{gathered} \Rightarrow(129750)/(100000)=(1+r)^4 \\ \Rightarrow1+r=\sqrt[4]{(129750)/(100000)} \\ \Rightarrow r=\sqrt[4]{(129750)/(100000)}-1 \\ \Rightarrow r=0.067276\ldots \\ \Rightarrow r\approx0.0673 \\ \Rightarrow r\approx6.73percent \end{gathered}`

The answer is, approximately, 6.73%