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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
Solution
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
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