On what sum will the compound interest at 5% per annum for two years c

1.	On what sum will the compound interest at 5% per annum for two years compounded annually be 1,640
Answer» Step-by-step EXPLANATION: Compound Interest (CI) = 1640 Rate = 5% TIME = 2 years Compound Interest = Amount - PRINCIPAL $\rm Amount = P\bigg(1 + \dfrac{r}{100}\bigg)^{n}$ $\rm So, CI = P\bigg(1 + \dfrac{r}{100}\bigg)^{n} - P$ $\rm \dashrightarrow 1640= P\bigg(1 + \dfrac{5}{100}\bigg)^{2} - P$ $\rm \dashrightarrow 1640= P\bigg( \dfrac{100 + 5}{100}\bigg)^{2} - P$ $\rm \dashrightarrow 1640= P\bigg( \dfrac{105}{100}\bigg)^{2} - P$ $\rm \dashrightarrow 1640= P\bigg( \dfrac{21}{20}\bigg)^{2} - P$ $\rm \dashrightarrow 1640= P\times \dfrac{441}{400}- P$ $\rm \dashrightarrow 1640= P \bigg[ \dfrac{441}{400}- 1 \bigg]$ $\rm \dashrightarrow 1640= P \times \dfrac{441 - 400}{400}$ $\rm \dashrightarrow 1640= P \times \dfrac{41}{400}$ $\rm \dashrightarrow P = 1640 \times \dfrac{400}{41}$ $\rm \dashrightarrow P = 16000$ $\dashrightarrow \underline{\boxed{\bf Principal = Rs.16000}}$