Question

Find the rate of interest if the s.I. For 3 years is rs. 1200 and c.I. For 2 years is rs. 860

Answer 1

please see the attachment

Answer 2

The rate of interest is 15%.

Explanation:

Formula for simple interest : $I=Prt$

Compound interest = $CI=P((1+r)^t-1)$

, where P = principal amount , t is time and r is rate of interest.

As per given , we have

$1200=Pr(3)\\\\\Rightarrow\ P=\dfrac{1200}{3r}=\dfrac{400}{r}$                        (1)

Also, $860=P((1+r)^2-1)$

Put value of P from (1) in this , we get

$860 =(\dfrac{400}{r})(1+r^2+2r-1)\\\\\Rightarrow\ 860 =(\dfrac{400}{r})(r^2+2r)\\\\\Rightarrow\ \dfrac{860}{400} =(\dfrac{1}{r})r(r+2)=(r+2)\\\\\Rightarrow\ 2.15} =r+2\\\\\Rightarrow\ r=2.15-2=0.15$

In % , r= 0.15 x 100 =15%

Hence, the rate of interest is 15%.

# Learn more :

The C.I. on a certain sum for 2 years is Rs.410 and S.I. is Rs.400. The rate of interest per annum is ______________.

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