Question

Find the Compound interest on Rs.30, 000 at 12% p.a for 2years.

Answer 1

Hint: We have been given Principal, time and rate of interest. Substitute them in the equation of amount in compound interest . Now find the Compound interest by subtracting the given principle from the amount we found.

Complete step-by-step solution -
Compound interest is the interest calculated on the principal and the interest accumulated over the previous periods. If we see that the interest increases for successive years then that interest charged by the bank is compound interest and not simple interest.
Compound interest is different from simple interest, where interest is not added to the principal while calculating the interest during the next period. To understand the compound interest we need to do its mathematical calculation. To calculate compound interest we need to know the amount and principal.
Compound interest = Amount – Principal. – (1)
\[A=P{{\left( 1+\dfrac{R}{100} \right)}^{t}}-(2)\]
Where, A = amount
P = Principal
R = Rate of interest
n = Number of times interest is compounded per year.
Now we have been given, P = Rs.30, 000, R = 12%, t = 2 years.
Let us substitute these values in equation (2).
\[\begin{align}
  & A=30000{{\left( 1+\dfrac{12}{100} \right)}^{2}} \\
 & A=30000{{\left( 1+0.12 \right)}^{2}} \\
 & A=30000{{\left( 1.12 \right)}^{2}}=30000\times 1.12\times 1.12 \\
\end{align}\]
A = Rs.37632.
Thus we got the amount. Now let us calculate compound interest.
Compound interest = Amount – Principal
                                    = 37632 – 30000
                                    = Rs.7632
Thus we got compound interest as Rs.7632.

Note: If we are calculating amount of 1 year, then, \[A=P{{\left( 1+\dfrac{R}{100} \right)}^{1}}=P+\dfrac{PR}{100}\].
\[\therefore \] Compound Interest \[=\left( P+\dfrac{PR}{100} \right)-P=\dfrac{PR}{100}-(1)\]
We know that Simple Interest = \[\dfrac{PR}{100}\].
For T = 1 year, \[S.I=\dfrac{PR}{100}-(2)\].
From this we can say that the interest rate for the first year in compound interest is the same as that in case of simple interest i.e. \[\dfrac{PR}{100}\]. Other than the first year, the interest compounded annually is always greater than in case of simple interest.