Question

Ashima took a loan of Rs 1,00,000 at 12% p.a. compounded half-yearly. She paid Rs 1,12,360. If (1.06)² is equal to 1.1236, then the period for which she took the loan is ______.

Options

• 2 years

• 1 year

• 6 months

• `1 1/2` years

Answer 1

Ashima took a loan of Rs 1,00,000 at 12% p.a. compounded half-yearly. She paid Rs 1,12,360. If (1.06)² is equal to 1.1236, then the period for which she took the loan is 1 year.

Explanation:

Given, principal (P) = Rs. 100000

Rate of interest (R%) = 12% per annum compounded half-yearly

Let m be the time period,

Amount paid = Rs. 112360

We know that,

Amount, when interest is compounded half-yearly

i.e. `A = P(1 + R/200)^(2n)`, where n = time period

⇒ `112360 = 100000(1 + 12/200)^(2n)`

⇒ `(53/50)^(2n) = 112360/100000`

⇒ `(53/50)^(2n) = 2809/2500`

⇒ `(53/50)^2 = (53/50)^(2n)`

On comparing both sides, we get

2n = 2

⇒ n = 1

So, the time period is 1 year.

Hence, 1 year