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Ashwin took a loan of Rs.100000 at 12% p.a. compounded for 6 months. He paid Rs.112360.What was the period for which he took the loan?

$Take 1.06 2 = 1.1236.$

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Detailed Solution

From the given data, we have,
Principal amount = Rs.100000
Interest rate = 12%
Total amount paid = Rs.112360
Let the time period be ‘t’.
The formula for compound interest if the interest is compounded for 6 months is given by,

C . I . = P 1 + R 200 2 t − P

We know that,
Total Amount = Principal Amount + C.I.

⇒ 112360 = 100000 + 100000 1 + 12200 2 t − 100000

⇒ 112360 = 100000 1 + 12200 2 t

⇒ 1.12360 = 1 + 12200 2 t ⇒ 1.06 2 = 1 + 12200 2 t

⇒ 1.06 2 = 1.06 2 t

On comparing the powers of the above equation, we get,

2 t = 2 ⇒ t = 1

Thus the period for which Ashwin took the loan is 1 year.
Hence, option (1) is correct.

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