Find the amount and the compound interest on ₹5000 at 10% p.a. for $1\dfrac{1}{2}$ years, compound interest reckoned semi-annually.

Since, compound interest is reckoned semi-annually,

rate = $\dfrac{10\%}{2}$ = 5%.

n (no. of conversion periods) = 3 half-years.

$\therefore A = P\Big(1 + \dfrac{r}{100}\Big)^n \\[1em] = ₹5000 \times \Big(1 + \dfrac{5}{100}\Big)^3 \\[1em] = ₹5000 \times \Big(\dfrac{105}{100}\Big)^3 \\[1em] = ₹5000 \times \Big(\dfrac{21}{20}\Big)^2 \\[1em] = ₹5000 \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20} \\[1em] = ₹5000 \times \dfrac{9261}{8000} \\[1em] = ₹5788.125$

C.I. = Amount - Principal = ₹5788.125 - ₹5000 = ₹788.125

Hence, amount = ₹5788.125 and compound interest = ₹788.125