Question

Rachna borrowed a certain sum at the rate of $15\%$ per annum. If she paid at the end of two years Rs. 1290 as interest compounded annually, find the sum she borrowed.

Answer 1

C.I = Rs. 1290
Rate (R) $=15\%$ p.a
Period (n) = 2 years
Let sum (P) = Rs. 100
Then $C.I=P[{(1+\frac{R}{100})}^n-1]$
C.I $=Rs.100[{(1+\frac{15}{100})}^2-1]$
$=Rs.100[{(1+\frac{15}{100})}^2-1]$
$=Rs.100[{\left(\frac{23}{20}\right)}^2-1]=Rs.100[\frac{529}{400}-1]$
$=Rs.\frac{100(529-400)}{400}=Rs.\frac{129}{4}$
If C.I. is $Rs.\frac{129}{4}$, then principal = Rs. 100
If C.I is Re. 1, then principal $=Rs.100\times \frac{4}{129}$
and if C.I is Rs. 1290, then principal
$=Rs.100\times \frac{4}{129}\times 1290=Rs.4000$
$\therefore$ Sum = Rs. 4000