Question

What rate of interest compounded annually is required to triple an investment in 5 years?

Short answer

The annual rate of interest required to triple the principal in 5 years is 24.57%

Step-by-step solution

Step 1. Given Information

Given certain amount is tripled after 5 years by compounding annually. The rate of interest at which the amount is compounded is to be determined.

Step 2. Calculation

According to the compound interest formula, the amount A after t years for the principal P with an annual rate of interest r compounded n times per year is$A=P{\left(1+\frac{r}{n}\right)}^{nt}$

Here let the principal be P.

Since the amount is tripled,$A=3P$

Since the amount is tripled after 5 years, $t=5$

And since the interest is compounded annually, $n=1$

Plugging the values to determine r:

$$\begin{gathered} A=P{\left(1+\frac{r}{n}\right)}^{nt} \\ 3P=P{\left(1+\frac{r}{1}\right)}^{\left(1\right)\left(5\right)} \\ {\left(1+r\right)}^5=3 \\ 1+r=\sqrt[5]{3} \\ 1+r=1.24573... \\ r=1.24573...-1 \\ r=0.24573... \end{gathered}$$

So the rate of interest in decimal form is 0.24573...

Therefore the interest rate is 24.57% (approximately)

Step 3. Conclusion

The annual rate of interest required to triple the principal in 5 years is 24.57%