Concept of Compound Interest-06

Question: If the CI on a certain sum for 2 years at 3% be Rs.101.50, what would be the SI? [Ans. (d) Rs. 100]

(a) Rs. 90   (b) Rs. 150   (c) Rs. 200   (d) Rs. 100   (e) None of these

Solution:

Detailed Explanation:

First Method: If Rs.100 is the principal, then Rs.3 is the SI for each of the two years; as the rate of compound interest is 3% pan.

SI in two years is Rs.6, that is,6%

The difference for the first year is 0.

The difference for the second year is 3% of Rs.3 = 0.09, that is 0.09%

The compound interest for the first year = 6.09%

Given that

                                 6.09% ≡ Rs.101.50 (given)                    

                                      6% ≡? = Rs.100 Ans.

Second Method: Options method is the best method; when SI or principal is to be determined.

SI can never be greater than CI, so Rs. 150 and Rs. 200 cannot be SI for the CI of Rs. 101.09

If Rs. 90 is the SI for two years, then Rs.45 will be the SI for the first year. The difference for the second year is 3% of Rs. 45 = Rs. 1.35.So, CI will be Rs.91.35, which is not true.

If Rs. 100 is the SI for two years, then Rs.50 will be the SI for the first year. The difference for the second year is 3% of Rs. 50 = Rs. 1.50.So, CI will be Rs.101. 50, which is true. Hence, Rs. 100 is the answer.