Concept of Compound Interest-04

Question: If the simple interest on a certain sum of money for 3 years at 5% is Rs. 150, find the corresponding CI.  [Ans. (a)  Rs. 157.625]

(a) Rs. 157.625 (b) Rs. 167.26 (c) Rs. 150.425 (d) Rs. 155.52 (e) None of these

Solution:

Detailed Explanation:

Concept: In compound interest (CI), amount for the first compounding period becomes principal for the next compounding period. Again, amount for the second compounding period becomes principal for the third compounding period, and so on.

Difference between CI and SI for the first compounding period is always zero. The difference between CI and SI for the second compounding period, (which is also the difference between CI and SI for two compounding period), is the Interest of

the SI of the first compounding period.

The difference between CI and SI for the third compounding period, (which is also the difference between CI and SI for the first three compounding periods), is the CI of the first two compounding periods.  

Solution: Given that the simple interest on a certain sum of money for 3 years at 5% is Rs. 150, so Rs. 50 is the SI for each the three years.

For the first year, there is no difference between CI and SI. For the second year, the difference between CI and SI is 5% of Rs. 50 = Rs. 2.5

The difference between CI and SI for the third year = 5% of [Rs. 50 + Rs. 50 + Rs. 2.5] = Rs. 2.5+ Rs. 2.5+ Rs. 0.125 = Rs. 5.125

The total difference between CI and SI in three years = Rs. 2.5 + Rs. 5.125 = Rs. 7.625

Therefore, the corresponding CI for in three years = Rs. 150 + Rs. 7.625 + Rs.157.625 Ans.

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