Question : Rs. 6000 is lent at the rate of 8% per annum on compound interest (compounded quarterly). What will be the compound interest of 6 months?
Option 1: Rs. 268.60
Option 2: Rs. 190.50
Option 3: Rs. 164.60
Option 4: Rs. 242.40
Correct Answer: Rs. 242.40
Solution :
When compounded annually, where $A$ is the total amount, $P$ is the principal amount, $R$ is the rate of interest per annum (in decimal), and $T$ is the time in years.
$\mathrm {A= P(1+\frac{R}{4})^{4T}}$
Given that: $P$ = Rs. 6000, $R$ = 8% = 0.08 and $T$ = 6 months = 0.5 years
$\mathrm {A= 6000(1+\frac{0.08}{4})^{4 \times0.5}}\mathrm {= 6000(1.02)^{2}}=\mathrm { 6242.40}$
$\therefore$ Compound interest = A – P = 6242.40 – 6000 = Rs. 242.40
Hence, the correct answer is Rs. 242.40.
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