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Find the difference between the compound interest and simple interest. On a sum of Rs. 50,000 at $10 %$ per annum for 2 years.

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Rs.500.

Rs.400.

Rs.700.

Rs.570.

answer is A.

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Detailed Solution

Given,

Principal (P) = Rs 500 00 Rate (R) = 10 ​ ​ % ​ ​ p .a . Time (T) = 2 years

The formula to calculate the amount is given by

A = P 1 + R 100 n ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (1)

Substitute the given value in equation (1) and solve for amount A,

⇒ A = 50000 1 + 10100 2 ⇒ A = 500001101002 ⇒ A = Rs 60500

Evaluate the compound interest C.I.,

⇒ C . I . = A − P ⇒ C . I . = 6050050000 ⇒ C . I . = Rs 10500

Find the simple interest,

⇒ S . I . = P R T 100 ⇒ S . I . = 50000 × 10 × 2 100 ⇒ S . I . = Rs 10000

Calculate the difference amount between C.I. and S.I.,

⇒ C . I . − S . I . = 10500 − 10000 ⇒ C . I . − S . I . = Rs 500

Hence, the difference amount between C.I. and S.I is Rs 500.
Hence, the correct option is 1.

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