Question

Question 8

Ashima took a loan of Rs 100000 at 12% per annum compounded half-yearly. She paid Rs 112360. If $(1.06{)}^2$ is equal to 1.1236, then the period for which she took the Loan is
(a) 2 yr
(b) 1 yr
(c) 6 months
(d)$1\frac{1}{2}yr$

Answer 1

Given, principal (P) = Rs. 100000
Rate of interest (R%) = 12% per annum compounded half-yearly
Let m be the time period.
$\because$ Amount paid = Rs.112360
We know that,
Amount, when interest is compounded half - yearly
i.e. $A=P{(1+\frac{R}{200})}^{2n}$, where n - time period
$\Rightarrow 112360=100000{(1+\frac{12}{200})}^{2m}\Rightarrow {\left(\frac{53}{50}\right)}^{2m}=\frac{112360}{100000}\Rightarrow {\left(\frac{53}{50}\right)}^{2n}=\frac{2809}{2500}\Rightarrow {\left(\frac{53}{50}\right)}^2={\left(\frac{53}{50}\right)}^{2n}$
On comparing both sides, we get
2n = 2
$\Rightarrow$ n = 1
So, the time period is 1 yr.