# Find the compound interest on Rs. 6,000 for 1 year at the rate of 4% per annum if the interest is a) Compounded half-yearly b) compounded quarterly

Given:

Principal $P=Rs.\ 6000$

Time $T=1\ year$

Rate of interest $r=4 \%$

To do:

We have to find the compound interest when the rate of interest is

a) Compounded half-yearly

b) compounded quarterly

Solution:

(a) Time $= 1$ year

Rate of interest $=4 \%$ per annum compounded half-yearly

Number of compounds $=2$

Amount $= P(1+\frac{\frac{r}{2}}{100})^{nT}$

$= 6000(1+\frac{\frac{4}{2}}{100})^{2 \times 1}$

$= 6000(\frac{102}{100})^2$

$= 6000(1.02)^2$

$=Rs.\ 6242.20$

Compound Interest $=$ Amount $-$ Principal

$=Rs.\ (6242.20-6000)$

$=Rs.\ 242.20$

(b) Time $= 1$ year

Rate of interest $=4 \%$ per annum compounded quarterly

Number of compounds $=4$

Amount $= P(1+\frac{\frac{r}{4}}{100})^{nT}$

$= 6000(1+\frac{\frac{4}{4}}{100})^{4 \times 1}$

$= 6000(\frac{101}{100})^4$

$= 6000(1.01)^4$

$=Rs.\ 6243.62$

Compound Interest $=$ Amount $-$ Principal

$=Rs.\ (6243.62-6000)$

$=Rs.\ 243.62$