Question

Find the compound interest, correct to the nearest rupee, on Rs. 2400 for $2\dfrac{1}{2}$ years at 5 percent per annum.

Answer 1

- Hint: Here, we will calculate compound interest for 2 years and then simple interest for $\dfrac{1}{2}$ year by using formula of compound interest (CI) $=P{{\left( 1+\dfrac{R}{100} \right)}^{N}}$ and simple interest (SI) $=\dfrac{PRN}{100}$ .

Complete step-by-step solution -

Now, first we will know about compound interest and simple interest.
Simple interest is based on principal amount whereas compound interest is based on principal amount and the interest compounded for a cycle of period.
CI $=P{{\left( 1+\dfrac{R}{100} \right)}^{N}}$
Where P (principal amount) $=$ Rs. 2400
R (Rate of interest) $=$ 5%
N (number of period) $=$ 2 years
So, finding compound interest by putting all the value, we get
CI $=2400{{\left( 1+\dfrac{5}{100} \right)}^{2}}$
$=2400{{\left( 1+0.05 \right)}^{2}}$
$=2400{{\left( 1.05 \right)}^{2}}$
$=2646$ Rs.
Now, to calculate interest we will subtract value of principal amount from compound interest(CI) which we will get as: CI $-$ P
$=2646-2400\Rightarrow Rs.246$
Now, this Rs.2646 will become the principal amount for $\dfrac{1}{2}$ year. So, we will calculate here simple interest as the whole year is not completed. We want to calculate for half the year only. So,
SI $=\dfrac{PRN}{100}$
Here all the parameters are the same as that of CI.
$=\dfrac{2646\times 5\times \dfrac{1}{2}}{100}$
$=\dfrac{1323\times 5}{100}$
$=1.323\times 5$
$=66.15$ Rs.
So, we have simple interest of Rs. 66.15
Now adding both the interests to get total interest for $2\dfrac{1}{2}$ years $=66.15+246$
$=Rs.312.15$
Thus, the nearest rupee is Rs. 312.

Note: We can also use the method by finding the amount using the formula for finding amount as Amount $=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}$ and substituting $P=2400,r=5$ and $t=\dfrac{5}{2}$ . Then we can compute the CI as $CI=Amount-P$ . There are chances of making mistakes while taking r as 0.05 instead of 5. Also, for finding CI adding Principal amount to the amount instead of subtracting it. So, be careful with this silly mistakes.