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Amit borrowed Rs. 16000 at $1712 %$ per annum simple interest. On the same day, he lent it to Ashu at the same rate but compounded annually. What does he gain at the end of 2 years?

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Rs.454

Rs.400

Rs.490

Rs.410

answer is C.

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Detailed Solution

Given,

Principal (P) = Rs 160 00 Rate (R) = 1712 ​ ​ % ​ ​ p .a . Time (T) = 2 years

The formula to compute the simple interest is given by

S . I . = P R T 100 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (1)

Substitute the given value in equation (1) and solve the simple interest paid by Amit,

⇒ S . I . = 16000 × 17.5 × 2 100 ⇒ S . I . = Rs 5600

The formula to calculate the amount is given by

A = P 1 + R 100 T ⋅ ⋅ ⋅ ⋅ ⋅ (2)

Substitute the given value in equation (2) and solve the amount A gained by Amit,

⇒ A = 16000 1 + 17.5 100 2 ⇒ A = 16000 117.5 100 2 ⇒ A = Rs 22090

Evaluate the compound interest,

C . I . = A − P ⇒ C . I . = 22090 − 16000 ⇒ C . I . = Rs 6090

Therefore, Total gained by Amit at the end of 2 years,

Total gain = 6090 − 5600 ⇒ Rs 490

Hence, the total gain at the end of two years is Rs 490.
Hence, the correct option is 3.

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