Question

On what sum will the compound interest at 5% per annum for two years compounded annually be 1,640​

Answer 1

Step-by-step explanation:

Compound Interest (CI) = 1640

Rate = 5%

Time = 2 years

Compound Interest = Amount - Principal

$\rm Amount = P\bigg(1 + \dfrac{r}{100}\bigg)^{n}$

$\rm So, CI = P\bigg(1 + \dfrac{r}{100}\bigg)^{n} - P$

$\rm \dashrightarrow 1640= P\bigg(1 + \dfrac{5}{100}\bigg)^{2} - P$

$\rm \dashrightarrow 1640= P\bigg( \dfrac{100 + 5}{100}\bigg)^{2} - P$

$\rm \dashrightarrow 1640= P\bigg( \dfrac{105}{100}\bigg)^{2} - P$

$\rm \dashrightarrow 1640= P\bigg( \dfrac{21}{20}\bigg)^{2} - P$

$\rm \dashrightarrow 1640= P\times \dfrac{441}{400}- P$

$\rm \dashrightarrow 1640= P \bigg[ \dfrac{441}{400}- 1 \bigg]$

$\rm \dashrightarrow 1640= P \times \dfrac{441 - 400}{400}$

$\rm \dashrightarrow 1640= P \times \dfrac{41}{400}$

$\rm \dashrightarrow P = 1640 \times \dfrac{400}{41}$

$\rm \dashrightarrow P = 16000$

$\dashrightarrow \underline{\boxed{\bf Principal = Rs.16000}}$