Question

What is the difference between the compound interests on $\text{Rs}10,000$ for $1\frac{1}{2}$ years at $4\%$ per annum compounded yearly and half-yearly?

• A. $\text{Rs}4.04$
• B. $\text{Rs}4.08$
• C. $\text{Rs}4.12$
  
• D. $\text{Rs}5$

Answer 1

The correct option is B $\text{Rs}4.08$

C.I. when interest is compounded annually but time is given in fraction $\left(t\frac{a}{b}\right)$ years, then

$=P{(1+\frac{R}{100})}^t\times (1+\frac{\frac{a}{b}\times R}{100})-P$

$=[10000\times {(1+\frac{4}{100})}^1\times (1+\frac{\frac{1}{2}\times 4}{100})]-10000$

$\Rightarrow$ C.I. when interest is compounded yearly $=10000\times \frac{26}{25}\times \frac{51}{50}-10000$

$\therefore$ C.I. when interest compounded yearly $=10608-10000=\text{Rs.}608$

C.I. when interest is compounded half-yearly

$=P{(1+\frac{R}{100\times 2})}^{2T},$ where $T$ is the number of years

$=[10000\times {(1+\frac{4}{2\times 100})}^3]-10000$

$\Rightarrow$ C.I. when interest is compounded half-yearly $=10000\times {\left(\frac{51}{50}\right)}^2-10000$

$\Rightarrow$ C.I. when interest is compounded half-yearly $=10612-10000=\text{Rs}612.08$

$\therefore$ Difference $=612.08-608=\text{Rs}4.08$