Question

Find the total amount and total interest after forty years if the interest is compounded every twenty years.

Principal = ₹50{,}000=₹50,000equals, ₹, 50, comma, 000


Rate of interest = 0. 5 \%=0. 5%equals, 0, point, 5, percent per annum

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\mathbb{R}50000\\ r=rate\to 0.5\%\to (0.5)/(100)\dotfill &0.005\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &20 \end{cases}`

`A = 50000\left(1+(0.005)/(1)\right)^(1\cdot 20)\implies A=50000(1.005)^(20) \implies \boxed{A \approx 55244.78} \\\\\\ 55244.78~~ - ~~50000 ~~ \approx ~~ \stackrel{earned~interest}{\boxed{5244.78}}`