Question

There is a $60\%$ increase in an amount in $6$ years at simple interest. What will be the compound interest on $Rs.12,000$ after $3$ years at the same rate?

• A. $Rs.2160$
• B. $Rs.3120$
• C. $Rs.3972$
• D. $Rs.6240$

Answer 1

The correct option is C $Rs.3972$

For first case:

Given, Principal $P=Rs.12,000$

Rate of interest $=R$

Time $T=6years$

If there is a $60$% increase in an amount in $6$ years at simple interest, then

$SI=60\%ofP$

$SI=\frac{60P}{100}$

Now,

$Interest=\frac{PTR}{100}$

$\Rightarrow \frac{60P}{100}=\frac{P\times 6\times R}{100}$

$\Rightarrow \frac{60}{100}=\frac{6\times R}{100}$

$\therefore R=10$%

Now Compound interest on $Rs.12000$ for $3$ years at the rate $10$% is

$C.I=P{(1+\frac{R}{100})}^n-P$

$⟹C.I=12000{(1+\frac{10}{100})}^3-12000$

$⟹C.I=12000{\left(\frac{11}{10}\right)}^3-12000$

$⟹C.I=12000\left(\frac{1331}{1000}\right)-12000$

$⟹C.I=15972-12000$

$\therefore C.I=Rs.3972$

Option C is correct.