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.