A sum amounts to Rs. 756.25 at $10 %$ per annum in 2 years, compounded annually. Find the sum.

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Rs 681

Rs 245.

Rs 725.

Rs 625.

answer is C.

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Detailed Solution

Given,
Interest rate, r = 10 % per annum,
Time period, t = 2 years,
Future value, A = Rs 756.25
Let P be the initial investment or principal amount that is compounded.
We have

A = P 1 + r 100 t

Substitute A = 756.25, r = 10 and t = 2 above.

⇒ 756.25 = P 1 + 10100 2

Solve for P

⇒ 756.25 = P 1.1 2

⇒ 756.25 = 1.21 P ⇒ P = 756.25 1.21 ⇒ P = 625

Thus, the required sum is Rs 625.
Hence, the correct option is 3.

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