Question

A sum of money triples itself in 20 years at simple interest. Find the rate of interest?

• A. $5\%$
• B. $15\%$
• C. $12\%$
• D. $10\%$

Answer 1

The correct option is D $10\%$

Let, principal (starting amount) $=P$
then, total amount $=3P$
Given, Time period = 20 years

We get the total amount by adding the simple interest to the principal.
$\text{Amount = Principal + Simple interest}$
$\Rightarrow 3P=P+\text{Simple interest}$
$\Rightarrow 3P-P=\text{Simple interest}$
$\Rightarrow \text{Simple interest}=2P\dots \left(i\right)$

Also, $\text{Simple interest}=\frac{PRT}{100}$
where, P = Principal, R = Rate of interest (expressed in $\%$ per annum) and T = time period (in years)
$\Rightarrow \text{Simple Interest}=\frac{P\times R\times 20}{100}\dots \left(ii\right)$

From $\left(i\right)$ and $\left(ii\right),$ we get
$\Rightarrow \frac{P\times R\times 20}{100}=2P$

Cross multiplying, we get
$P\times R\times 20=2P\times 100$

Dividing both the sides by $P,$ we get
$R\times 20=2\times 100$
$R\times 20=200$

Dividing both the sides by $20,$ we get

$\Rightarrow R=\frac{200}{20}$

Simplify and cancel out common factors, we get
$\Rightarrow R=\frac{20\times 10}{20}$
$\Rightarrow R=10\%$

Hence, rate of interest is $10\%.$