Answer
$11.61\%.$
Work Step by Step
According to the Compound Interest Formula, where $P$ is the principal, the amount deposited, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded annually, $t$ is the number of years, $A$ is the amount the loaner gets back after $t$ years:
$A=P\cdot(1+\frac{r}{n})^{n\cdot t}.$
The investment is compounded annually, hence $n=1$.
Thus, the formula above becomes:
$A=P\cdot(1+\frac{r}{1})^{1\cdot t}\\ A=P\cdot(1+r)^{t}.$
The given situation has
$t=10$ years
$A=3P$ because the investment triples after $5$ years.
Using the formula above gives: $3\cdot P=P\cdot(1+r)^{10}\\3=(1+r)^{10}.\\\sqrt[10] {3}=\sqrt[10] {(1+r)^{10}}\\\sqrt[10] 3=1+r\\r=\sqrt[10] 3-1$.
Use a calculator to obtain:
$r=\sqrt[10] 3-1\\r=1.116123-1\\r=0.116123\\\approx11.61\%$
