Question

On a certain sum and at a certain rate percent, the simple interest for the first year is Rs. 270, and the compound interest for the first two years is Rs. 580.50. Find the sum and the rate percent.

Answer 1

S.I for $1$ year$=$Rs$270$

$\therefore$C.I for $1$ year$=$Rs.$270$ [For 1st year:C.I=S.I]

C.I for 2 years=Rs.580.50

$\therefore$ C.I for 2nd year=$580.50-270.00=Rs.310.50$

Difference between the C.I of two successive years$=310.50-270=Rs.40.50$

$\therefore$Rate of interest can be calculated using the Simple Interest formula i.e

$S.I.=\frac{P\times R\times T}{100}$

$\Rightarrow R=\frac{100\times 40.50}{270\times 1}=15$%

Now to calculate the sum or Principal

$S.I=\frac{P\times R\times T}{100}$

$\therefore P=\frac{S.I\times 100}{R\times T}$

$\Rightarrow P=\frac{270\times 100}{15\times 1}$

$\Rightarrow P=Rs.1800$