The difference between the S.I. and C.I. on a certain sum of money for 2 years at 4 per annum is Rs.20. Find the sum.

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Rs 12534

Rs 12500

Rs 17500

Rs 12560

answer is B.

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Detailed Solution

Interest rate, r = 4%, Time period, t = 2 years, Difference between S.I. and C.I. is 20
Calculate the simple and compounded interest.
Simple interest is given by,

S I = P r 100 t

Now substitute, r = 4, t = 2

⇒ S I = P 41002 ⇒ S I = 0.08 P

Compounded interest is given by,

C F = P 1 + r 100 t − P

Now substitute, r = 4, t = 2

⇒ C F = P 1 + 4100 2 − P ⇒ C F = P 1.04 2 − P ⇒ C F = 1.0816 P − P ⇒ C F = 0.0816 P

Calculate P It is given that, C.I. – S.I. = 20
Substitute the value of CI and SI above

⇒ 0.0816 P − 0.08 P = 20 ⇒ 0.0016 P = 20 ⇒ P = 20 0.0016 ⇒ P = 12500

Thus, the required sum is Rs 12500.
Hence, the correct option is 2.

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