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:
[tex]\begin{gathered} Debt=100000(1+r)^4 \\ \Rightarrow129750=100000(1+r)^4 \end{gathered}[/tex]Solving for r
[tex]\begin{gathered} \Rightarrow\frac{129750}{100000}=(1+r)^4 \\ \Rightarrow1+r=\sqrt[4]{\frac{129750}{100000}} \\ \Rightarrow r=\sqrt[4]{\frac{129750}{100000}}-1 \\ \Rightarrow r=0.067276\ldots \\ \Rightarrow r\approx0.0673 \\ \Rightarrow r\approx6.73percent \end{gathered}[/tex]The answer is, approximately, 6.73%
