Question

Calculate compound interest on ` 1000 over a period of 1 year at 10% per annum, if interest is compounded quarterly with easy explanation

Answer 1

To calculate compound interest,

First use the following formula to calculate the amount

$a= p(1 + \frac{r}{n} )^{nt}$

Then subtract principal from amount to get the compound interest.

Here,
P = 1000
rate, r = 10%
time, t = 1 year

it is compounded quarterly,
thus n = 1 ÷ 0.25 = 4

$A = p(1 + \frac{r}{4 \times 100} )^{nt} \\ \\ A= 1000(1 + \frac{10}{4 \times 100} )^{1 \times 4}$

$A = 1000(1 + 0.025)^{ 4} \\ \\ A = 1000 \times {1.025}^{4} \\ \\ A= 1103.8$

Amount = ₹1103.8

Compound Interest = 1103.8 - 1000 = ₹103.8

Answer 2

One year = 4 quarters

A=1000(1+(10/4)/100)^4

=1000(1+5/2*1/100)^4

=1000(1+1/40)^4

=1000(41/40)^4

=1000*2825761m/2560000

1*2825761/2560=1103.81

Ci=a:-P=1103.81-1000

=103.81 rupees.