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A sum of money, on compound interest, amounts to ₹5,290 in 2 years and to ₹6,083.50 in 3 years. If interest is compounded annually, then the rate of interest per annum is:
1632%
15%
14%
12%
15%
For compound interest, the ratio of amounts in consecutive years gives the growth factor for 1 year. The rate of interest is simply A2A3−A2×100.
Amount after 2 years = ₹5,290, Amount after 3 years = ₹6,083.50, compounded annually
Rate=(A1A2−1)×100
For compound interest, the ratio of amounts in consecutive years gives the growth factor for 1 year. The rate of interest is simply A2A3−A2×100.
Confusing compound interest with simple interest and attempting to use linear interest formulas.
Identify Given Amounts
Let the amount after 2 years be A1=₹5,290 and after 3 years be A2=₹6,083.50.
A1=5290,A2=6083.50
Calculate Interest for the 3rd Year
The interest earned during the 3rd year is the difference between the amount at 3 years and 2 years.
I3=6083.50−5290=793.50
Find the Rate of Interest
The interest of ₹793.50 is accrued on ₹5,290 in 1 year. Applying the rate formula:
R=5290793.50×100=15%
B is correct because the calculated rate of interest per annum is 15%.
In compound interest problems involving consecutive years, treat the amount at the earlier year as the principal for the succeeding year.
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