Question

What will be the difference between simple and compound interests at the rate of $10\%$p.a. on a sum of Rs $1000$ after $4$ years?

• A. Rs $64.10$
• B. Rs $40.40$
• C. Rs $32.10$
• D. Rs $31$

Answer 1

The correct option is A Rs $64.10$

$\Rightarrow$ $P=Rs.1000,R=10\%,T=4years$

$\Rightarrow$ $SimpleInterest=\frac{P\times R\times T}{100}$

$\Rightarrow$ $SimpleInterest=\frac{1000\times 10\times 4}{100}=Rs.400$

$\Rightarrow$ Now, $A=P(1+\frac{R}{100}{)}^T$

$\Rightarrow$ $A=1000(1+\frac{10}{100}{)}^4$

$\Rightarrow$ $A=1000\times \frac{110}{100}\times \frac{110}{100}\times \frac{110}{100}\times \frac{110}{100}=Rs.1464.10$

$\Rightarrow$ $Compoundinterest=A-P=1464.10-1000=Rs..464.10$

$\therefore$ $Compoundinterest-Simpleinterest=Rs.464.10-Rs.400=Rs.64.10$