Question

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

Answer 1

Given: $60\%$ increase in amount in 6 yrs at SI

To find : CI of Rs 12,000 after 3 yrs at

Same rate

We know that,

$SI=\frac{P\times R\times T}{100}$

Where, SI $=$ Simple interest

$P=$ Principle

$R=$ rate of interest

$t=$ time period

and $A=SI+P...\left(2\right)$

Where, $A=$ amount

Let principal be Rs.P

$A=P+60\%$ of P

$A=P+\left(\frac{60}{100}\right)P$

$A=\frac{8P}{5}...\left(1\right)$

also from eq (2)

$A=SI+P$ (putting value of A from

eq (1))

$\frac{8P}{5}=\frac{P\times R\times 6}{100}+P$

$\frac{8}{5}=\frac{6R}{100}+1$

$R=10\%...\left(3\right)$

for; compound interest

$A=P{(1+\frac{R}{100})}^n$

$n=$ time period

$A=12000{(1+\frac{10}{100})}^3$ [putting value of R from eq (3)]

$A=Rs\mathrm{15972...}\left(4\right)$

Compound Interest $=$ Amount $-$ Principal

(Putting value of A and P)

$=15972-12000$

$CI=Rs3972$