Find the amount and the compound interest on ₹100000 compounded quarterly for 9 months at the rate of 4% p.a.

Since rate of interest is 4% per annum, therefore rate of interest per conversion period (quarterly) = $\dfrac{1}{4} \times 4$ = 1%.

As the money is invested for 9 months, therefore,

n (the number of conversion periods) = $\dfrac{9}{3}$ = 3.

$\therefore A = P\Big(1 + \dfrac{r}{100}\Big)^n \\[1em] = ₹100000 \times \Big(1 + \dfrac{1}{100}\Big)^3 \\[1em] = ₹100000 \times \Big(\dfrac{101}{100}\Big)^3 \\[1em] = ₹100000 \times \Big(\dfrac{101}{100}\Big)^3 \\[1em] = ₹100000 \times \dfrac{101}{100} \times \dfrac{101}{100} \times \dfrac{101}{100} \\[1em] = ₹\dfrac{100000 \times 101 \times 101 \times 101}{1000000} \\[1em] = ₹\dfrac{1030301}{10} \\[1em] = ₹103030.10$

Compound interest = Final amount - Principal = ₹103030.10 - ₹100000 = ₹3030.10

Hence, amount = ₹103030.10 and compound interest = ₹3030.10.