Q.If interest is compounded every 6 months, then at an annual compound interest rate of 10%, what will be the compound amount and compound interest on ₹8000 for 1½ years?

Principal \((p) = ₹8000\) Time \((n) = 1\frac{1}{2}\) years \(= \frac{3}{2}\) years Rate of interest \((r) = 10\%\) Compounding period = \(\frac{12}{6} = 2\) times per year \(\therefore\) Compound amount after \(1\frac{1}{2}\) years: \(= p\left(1 + \frac{\frac{r}{2}}{100}\right)^{2 \times \frac{3}{2}}\) \(= 8000\left(1 + \frac{\frac{10}{2}}{100}\right)^3\) \(= 8000\left(1 + \frac{10}{200}\right)^3\) \(= 8000\left(1 + \frac{1}{20}\right)^3\) \(= 8000 \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20}\) \(= ₹9261\) \(\therefore\) Compound interest = \(₹9261 - ₹8000 = ₹1261\) So, the compound interest is ₹1261 and the total amount including interest is ₹9261.
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