A sum of money becomes Rs. 6720 after 2 years and Rs. 7392 after 3 years at compound interest. What is the rate of interest per annum?
10%
Under compound interest, the amount at the end of each year forms a geometric progression: each successive year's amount equals the previous year's amount multiplied by \(\left(1+\frac{r}{100}\right)\).
So the interest earned during the 3rd year is the difference between the 3-year amount and the 2-year amount: \(7392-6720=672\). This Rs. 672 is one year's interest computed on the 2-year amount of Rs. 6720.
Therefore the rate is \(r=\frac{672}{6720}\times100=10\%\).
Check: the ratio of consecutive amounts is \(\frac{7392}{6720}=\frac{11}{10}=1.10\), confirming a growth factor of \(1+\frac{10}{100}\).
Hence, the rate of interest is 10% per annum.
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