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The difference between the compound interest and simple interest on a certain sum for 2 years at $7.5 %$ per annum is Rs. 360 Find the sum.

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Rs 64820

Rs 82100

Rs 72611

Rs 64000

answer is D.

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Detailed Solution

Given,
Time period, t = 2 years,
Interest rate, r = 7.5% C.I. – S.I. = Rs 360 …… (1)
Here C.I. is the compound interest and S.I. is the simple interest.
Apply the compound interest and simple interest formula in equation (1).

⇒ C .I . − S .I . = 360 ⇒ P 1 + r 100 t − P − P r 100 t = 360

Now substitute, r = 7.5, t = 2

⇒ P 1 + 7.5 100 2 − P − P 7.5 100 2 = 360 ⇒ P 1.155625 − 1 − 0.15 P = 3600 ⇒ 155625 P − 0.15 P = 3600 ⇒ 0.005625 P = 360 P ⇒ 360 0.005625 P ⇒ P = 64000

Thus, the required sum is Rs 64000
Hence, the correct option is 4.

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