Question

Find the amount on the Rs. 20000 after 2 years if the rates of interest are 2% and 3% for successive years.

Answer 1

Hint: In this, we will use the formula of compound interest with a variable rate of interest.

Complete step-by-step solution -
If we have principal amount is P, rate of interest for successive years are $r_1, r_2, r_3.......$ then amount (A) is
$A=P\left( 1+\dfrac{{{r}_{1}}}{100} \right)\left( 1+\dfrac{{{r}_{2}}}{100} \right)\left( 1+\dfrac{{{r}_{3}}}{100} \right)............$
In given question P = Rs 20,000
$r_1$ =2%
$r_2$ =3%
So amount is
$\Rightarrow A=P\left( 1+\dfrac{2}{100} \right)\left( 1+\dfrac{3}{100} \right)$
$\Rightarrow A=20000\times \dfrac{102}{100}\times \dfrac{103}{100}$
$\Rightarrow A=20000\times \dfrac{102}{100}\times \dfrac{103}{100}$
$\Rightarrow A=21012$
So the amount on Rs. 20000 after 2 years if the rates of interest are 2% and 3% for successive years is Rs. 21012.

Note: In this case by the formula we will get the final amount. So we will not add it with the principal amount. In the case of simple interest, we only get interest. So for getting the final amount we need to add it with the principal.