At what rate percent p.a. compound interest would ₹80000 amount to ₹88200 in two years, interest being compounded yearly. Also find the amount after 3 years at the above rate of compound interest.

Let the rate of interest be r% per annum.

$A = P\Big(1 + \dfrac{r}{100}\Big)^n.$

Substituting value we get,

$\Rightarrow 88200 = 80000\Big(1 + \dfrac{r}{100}\Big)^2 \\[1em] \Rightarrow \dfrac{88200}{80000} = \Big(1 + \dfrac{r}{100}\Big)^2 \\[1em] \Rightarrow \dfrac{441}{400} = \Big(1 + \dfrac{r}{100}\Big)^2 \\[1em] \Rightarrow \Big(\dfrac{21}{20}\Big)^2 = \Big(1 + \dfrac{r}{100}\Big)^2 \\[1em] \Rightarrow 1 + \dfrac{r}{100} = \dfrac{21}{20} \\[1em] \Rightarrow \dfrac{r}{100} = \dfrac{21}{20} - 1 \\[1em] \Rightarrow \dfrac{r}{100} = \dfrac{21 - 20}{20} \\[1em] \Rightarrow \dfrac{r}{100} = \dfrac{1}{20} \\[1em] \Rightarrow r = \dfrac{1}{20} \times 100 \\[1em] \Rightarrow r = 5\%.$

After 3 years,

$A = ₹80000\Big(1 + \dfrac{5}{100}\Big)^3 \\[1em] = ₹80000 \times \Big(\dfrac{105}{100}\Big)^3 \\[1em] = ₹80000 \times \Big(\dfrac{21}{20}\Big)^3 \\[1em] = ₹80000 \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20} \\[1em] = ₹80000 \times \dfrac{9261}{8000} \\[1em] = ₹92610.$

Hence, the rate of interest = 5% per annum and amount after 3 years = ₹92610.