Question

Find the compound interest on ₹1000 at the rate of 10% per annum for 3 years.

Answer 1

Hint: Use the formula for amount given by $A = P{(1 + \dfrac{r}{{100}})^n}$
Where A = amount, P = principal, r = rate of interest per annum and n = no. of years
Then use the formula for compound interest given by Compound Interest = Amount - Principal
This will give us the required answer.

Complete step by step solution: Let us note down the given data.
The amount on which the interest is calculated is the principal and is denoted by P.
Thus, we have principal = P = ₹1000
Rate of interest = 10% per annum
The period of interest (in years) = 3 years
We can see that these conditions are satisfied here.
Let us write down the formula for calculating compound interest.
Compound Interest = Amount - Principal………….equation (1)
Thus, it can be seen that to calculate the compound interest, one needs to compute the amount first.
And the formula for computing this amount is as follows:
$A = P{(1 + \dfrac{r}{{100}})^n}$
Where A denotes the amount
So, let us quickly plug in the values of P, r and n in the above formula.
Thus, we get
\[ A = P{(1 + \dfrac{r}{{100}})^n} \\
   = 1000{(1 + \dfrac{{10}}{{100}})^3} \\
   = 1000{(1 + 0.01)^3} \\
   = 1000{(1.01)^3} \\
   = 1000 \times 1.030301 \\
   = 1030.301 \\ \]
So, the amount is ₹1030.301.
Now, substitute the values of amount and principal in equation (1).
Then, we have compound interest = 1030.301 - 1000 = 30.301
Hence the required compound interest is ₹30.301.

Note: Before proceeding onto using the formula, it is a must that you check if the values given are expressed in the expected units.
That is, one must remember that for such questions, we need to have an annual rate of interest and the period of interest must also be expressed in years.
If it is not the case, you can always convert them into the required format by dividing the rate of interest by 12 to obtain the annual rate and by dividing the given period by 12 to get the no. of years.