Question

What rate of interest compounded annually is required to triple an investment in 10 years?

Short answer

The annual rate of interest required to triple the principal in 10 years is 11.61%

Step-by-step solution

Step 1. Given Information

Given certain amount is tripled after 10 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 10 years, $t=10$

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

Plugging the values to determine r:

$$\begin{gathered} A=P{\left(1+\frac{r}{n}\right)}^{nt} \\ 3P=P{\left(1+\frac{r}{1}\right)}^{\left(1\right)\left(10\right)} \\ {\left(1+r\right)}^{10}=3 \\ 1+r=\sqrt[10]{3} \\ 1+r=1.11612... \\ r=1.11612...-1 \\ r=0.11612... \end{gathered}$$

So the rate of interest in decimal form is 0.11612...

There the interest rate is 11.61% (approximately)

Step 3. Conclusion

The annual rate of interest required to triple the principal in 10 years is 11.61%