Question

Find the compound interest on Rs. 20,000 at 10% per annum for 3 years.

Answer 1

Hint:- We had to only apply compound interest formula i.e. \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}\] directly to get the amount after 3 years and then subtract initial amount to get the compound interest for 3 years.

Complete step-by-step solution -
As we know that the principal amount is Rs. 20,000.
Rate of interest is 10% at annual rate.
And the rate of interest is compounded annually.
So, now we can apply compound interest formulas to find the amount after three years.
According to compound interest formula compound interest for t years is calculated as \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}\]where r is the annual rate of interest, t will be number of years after which we had to find the amount, P will be the principal amount and A will be the amount after t years.
So, according to the question,
P = Rs. 20,000
r = 10%
and t = 3 years.
So, putting all the values in the formula of compound interest we will get,
\[A = 20000{\left( {1 + \dfrac{{10}}{{100}}} \right)^3} = 20000{\left( {\dfrac{{110}}{{100}}} \right)^3}\]
So, \[A = 20000 \times \dfrac{{110}}{{100}} \times \dfrac{{110}}{{100}} \times \dfrac{{110}}{{100}} = \dfrac{{2 \times 110 \times 110 \times 110}}{{100}} = 26620\]
So, the amount after three years will be equal to Rs. 26,620.
Now the compound interest for three years will be = Amount after three years – Initial amount.
So, the compound interest for 3 years will be = Rs. 26,620 – Rs. 20,000 = Rs. 6,620
Hence, the compound interest for three years will be Rs. 6,620.

Note:- Whenever we come up with this type of question, we should note that simple interest and compound interest are not the same because simple interest is based on the principal amount of a loan or deposit. But in contrast, compound interest is based on the principal amount and the interest that accumulates on it every period. So, we had to put values in the compound interest formula i.e. \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}\] (where A is the amount invested, r is the rate of interest annually and t will be the total number of years) to get the amount after three years (A).