The difference between the compound and the simple interest of a sum for 2 years at 10 per annum whe...........

Quantitative Aptitude ( CCS) Compound Interest

The difference between the compound and the simple interest of a sum for 2 years at 10% per annum, when the interest is compounded annually, is Rs. 28. If the yearly interest were compounded half yearly, the difference in the two interest will be

Rs. 44

Rs. 28.35

Rs. 43.4

Rs. 43.29

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Explanation:

Time = 2 years, Rate = 10%
Case I: When interest compounded annually
2 years CI Rate % = 10 + 10 + (10 × 10)/100
2 years SI Rate % = 10 + 10 = 20%
According to the question,
(21 – 20)% of sum = Rs. 28
Sum = 29/1 × 100 = Rs. 2800
Case II: When interest is compounded half – yearly
Rate = 10/2 = 5%
Time = 2 × 2 = 4
Effective Rate % of CI for 2 half yearly
= 5 + 5 + (5 × 5)/100 = 10.25%
Effective Rate % of CI for 4 half yearly
= 10.25 + 10.25 + (10.25 × 10.25)/100
= 20.50 + 1.050625 = 21.55%
Effective rate % of SI for 4 years = 5 × 4 = 20%
Difference in Rate% = (21.55 - 20) = 1.55%
Required difference = 1.55/100 × 2800
= 43.4
Hence, Required Difference = Rs. 43.4