Question

Ashima took a loan of ₹1,00,000 at 12% per annum compounded half-yearly. She paid ₹1,12,360. If $(1.06{)}^2$ is equal to 1.1236, then find the period for which she took the loan.

Answer 1

Given, principal (P) = ₹1,00,000
Rate of interest (R%) = 12% per annum compounded half-yearly
Let m be the time period.
$\because$ Amount paid = ₹1,12,360
We know that,
Amount, when interest is compounded half - yearly
i.e. $A=P{(1+\frac{R}{200})}^{2n}$, where n - time period
$\Rightarrow 1,12,360=1,00,000{(1+\frac{12}{200})}^{2m}\Rightarrow {\left(\frac{53}{50}\right)}^{2m}=\frac{1,12,360}{1,00,000}\Rightarrow {\left(\frac{53}{50}\right)}^{2n}=\frac{2,809}{2,500}\Rightarrow {\left(\frac{53}{50}\right)}^2={\left(\frac{53}{50}\right)}^{2n}$
On comparing both sides, we get
2n = 2
$\Rightarrow$ n = 1
So, the time period is 1 yr.