Q.If the interest period is 6 months and the annual compound interest rate is 10%, determine the compound interest and the total amount for ₹16,000 in \(1\frac{1}{2}\) years.

Principal \((p) = 16000\) rupees,
Time \((n) = 1\cfrac{1}{2}\) years \(=\cfrac{3}{2}\) years
Rate of interest \((r) = 10\%\)
Interest period \(=\cfrac{12}{6} = 2\)

\(\therefore\) Compound amount after \(1\cfrac{1}{2}\) years
\(= p\left(1+\cfrac{\cfrac{r}{2}}{100}\right)^{2×\cfrac{3}{2}}\)
\(= 16000\left(1+\cfrac{\cfrac{10}{2}}{100}\right)^3\) rupees
\(= 16000\left(1+\cfrac{10}{200}\right)^3\) rupees
\(= 16000\left(1+\cfrac{1}{20}\right)^3\) rupees
\(= 16000 \times \cfrac{21}{20} \times \cfrac{21}{20} \times \cfrac{21}{20}\) rupees
\(= 18522\) rupees.

\(\therefore\) Compound interest \(= (18522 - 16000)\) rupees \(= 2522\) rupees

\(\therefore\) The compound interest will be \(2522\) rupees, and the total amount after interest will be \(18522\) rupees.
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