Compound Interest [चक्रवृद्धि ब्याज]-02]

Question: What will the compound interest be on Rs. 10000 at the rate of 4% per annum in 2 years, if the interest is compounded half-yearly? [4% प्रति वर्ष ब्याज की दर से 10000 रुपये का 2 वर्षों में चक्रवृधि ब्याज कितना होगा, यदि ब्याज अर्धवार्षिक संयोजित होता हो?]  [Ans. (b) Rs. 824.32]

(a) Rs. 636.80    (b) Rs. 824.32   (c) Rs. 912.86   (d) Rs. 828.82   (e) none of these

Solution: 

Detailed Explanation: Here, the principal is Rs. 10000. Time is 2 years, but interest is compounded half yearly; so no. of compounding period is 4(there are four “half years” in 2 years). Rate is given 4% par annum, the rate is 2% per compounding period.

The SI for each year is 2% of Rs. 10000 = Rs. 200 for each year. 

Again, the differences between CI and SI is to be calculated.

The difference for the first year is always zero.

Difference for the second year is 2% of Rs. 200 = Rs. 4

Difference for the third year is 2% of Rs. 400 + 2% of Rs. 4 =Rs. 8 + Rs. 0.08

Difference for the fourth year is 2% of Rs.600 + 2% of Rs. 12.08 = Rs. 12 + Rs. 0.24

So, the total differences is Rs. 24.32

And, CI = Rs. 800 + Rs. 24.32 = Rs. 824.32 Ans.