We will find the interest rate by using the following expression:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here A is the amount, P is the principal, r is the rate, n is the number of interest is compounded per unit t, and t is the time.
Now, we replace the values and solve for r:
[tex]2661.46=2500(1+\frac{r}{25})^{25}\Rightarrow\frac{2661.46}{2500}=(1+\frac{r}{12})^{12\cdot\frac{25}{144}}[/tex][tex]\Rightarrow\ln (\frac{2661.46}{2500})=\frac{25}{12}\text{ln}(1+\frac{r}{12})\Rightarrow0.062541\approx\frac{25}{12}\ln (\frac{x}{12}+1)\Rightarrow0.0300404\approx\ln (\frac{x}{12}+1)[/tex][tex]\Rightarrow\frac{x}{12}+1\approx1.0305\Rightarrow\frac{x}{12}\approx0.03404961\Rightarrow x\approx0.3215954[/tex]So, the annual interest rate was approximately 6.3%.
