Question

A sum of money invested at $8\%$ per annum amounts to Rs. $12,122$ in years. What will it amount to in $2$ years $8$ months at $9\%$ per annum?

Answer 1

We know that $SI=\frac{PRT}{100}$, and $S.I.=A-P$

Given, $R=8$%

$A=12122$ Rs.

$T=2$ years

Let $P=x$ Rs.

Then $12122-x=\frac{x\times 8\times 2}{100}$

$\Rightarrow 12122-x=x.\frac{16}{100}$

$\Rightarrow 12122-x=\frac{4x}{25}$

$\Rightarrow 12122-x=\frac{4x}{25}+x$

$\Rightarrow 12122=\frac{4x+25x}{25}$

$\Rightarrow 12122=\frac{29x}{25}$

$\Rightarrow \frac{12122\times 25}{29}=x$

$\therefore x=10450.$

After $2$ years $8$ month at $9$% per annum

$T=\frac{8}{3}$ years

$R=9$%

$P=10450$ Rs

$I=\frac{10450\times 8\times 9}{300}$

$=\frac{10450\times 24}{100}$

$=\frac{250800}{100}$

$I=2508$ Rs

$A=10450+2508=12958$ Rs.