Question

How many years does it take to double the sum of money at a simple interest rate of 5 percent per annum?
years

Answer 1

Let, principal (starting amount) $=P$
then, total amount $=2P$
Given, Rate of interest = 5%

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

Also, $\text{Simple interest}=\frac{PRT}{100}\dots \left(ii\right)$
where, P = Principal, R = Rate of interest (expressed in $\%$ per annum) and T = time period (in years)
From $\left(i\right)$ and $\left(ii\right),$ we get
$\Rightarrow \frac{P\times 5\times T}{100}=P$
Cross multiplying, we get
$P\times 5\times T=P\times 100$
Dividing both the sides by $P,$ we get
$5\times T=100$
Dividing both the sides by $5,$ we get
$T=\frac{100}{5}$
$\Rightarrow T=\frac{5\times 20}{5}$
$\Rightarrow T=20$ years