Question

16. Ajit borrowed 2,00.000 from a credit card company at 20% p.a. compounded quarterly.
Find the compound interest and the amount after one year.​

Answer 1

Given:

Principal value = 2,00,000

Rate of interest = 20% p.a. compounded quarterly.

To find:

The compound interest and the amount after one year.​

Solution:

Formula for amount is:

$A=P\left(1+\dfrac{r}{n}\right)^{nt}$

Where, P is principal, r is the rate of interest in decimal, n is the number of times interest compounded in an year and t is the number of years.

The interest is compounded quarterly. So, the value of n is 4.

Putting $P=200000,\ r=0.2,\ n=4,\ t=1$ in the above formula.

$A=200000\left(1+\dfrac{0.2}{4}\right)^{4(1)}$

$A=200000\left(1+0.05\right)^{4}$

$A=200000\left(1.05\right)^{4}$

$A=200000(1.21550625)$

$A=243101.25$

Therefore, the amount after one year is 2,43,101.25.

We know that the compound interest is the difference between amount and principal value. So,

$C.I.=A-P$

$C.I.=2,43,101.25-2,00,000$

$C.I.=43,101.25$

Therefore, the amount is 2,43,101.25 and the compound interest is 43,101.25.