Question
An investor put a sum at 14% per annum for 2 years
compounded annually. If instead the interest was compounded half yearly, he would have earned Rs. 112 more. What was the amount he invested?Solution
ATQ,
Let the principal be Rs. ‘P’.
When compounded annually:
CI = P(1 + 14/100)² – P = P[(1.14)² – 1] = P(1.2996 – 1) = 0.2996 × P
When compounded half-yearly:
CI = P(1 + 7/100)⁴ – P = P[(1.07)⁴ – 1] = P(1.3108 – 1) = 0.3108 × P
According to the question:
0.3108 × P – 0.2996 × P = 112
0.0112 × P = 112
P = 112 / 0.0112 = Rs. 10,000
Therefore, the invested amount is Rs. 10,000
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