Compound Interest [चक्रवृद्धि ब्याज]-01

Question: The difference between the compound interest and the simple interest on a certain sum of money at 12% per annum for 1 year is Rs. 36.00, the interest is compounded half-yearly. Find the sum. [12% प्रति वर्ष चक्रवृद्धि ब्याज की दर से किसी धन का एक वर्ष में साधारण ब्याज एवं चक्रवृद्धि ब्याज का अंतर 36 रूपये होता है, जबकि ब्याज अर्द्धवार्षिक संयोजित होता है. वह मूलधन क्या है?]   [Ans. (a) Rs. 10000]

(a) Rs. 10000 (b) Rs. 12000 (c) Rs.15000 (d) Rs.9000 (e) none of these

Detailed Explanation: Here the interest is compounded half-yearly and time is one year, so the number of compounding period is 2. Since the rate of interest is 12% per annum, to the rate per compounding period is 6%.

For the first year, there is no difference between SI and CI, because the principal in both the type of interests are the same. Difference is created from the 2^nd compounding period, because in the compound interest, principal is changed. The amount (principal and simple interest for the first year) becomes the principal for the second compounding period. But in SI, principal remains constant throughout the period.

Difference between SI and CI in two compounding periods is, in reality, the interest of simple interest created during the first compounding period.

First Method: Difference is given, 6% ≡ Rs. 36. Principal for this interest (difference) is SI for the first compounding period.

So, 6% ≡ Rs. 36. So, 100% ≡ Rs. 600. Rs. 600 is the SI for the first compounding period.

Again, 6% ≡ Rs. 600. Principal for this interest (SI for the first compounding period) is the principal to be determined.

So, 6% ≡ Rs. 600. So, 100% ≡ Rs. 10000. Ans.

Second Method: Using the formula,

Difference (CI - SI) for two years = Principal × (r/100)²

Or, 36 = Principal × (6/100)²

Principal = Rs. 10000 Ans.