Question

At what rate does the compound interest for rs. 1800 be rs. 378 in 2 years if interest has been calculated annually

Answer 1

Principle = 1800 rs

Simple Interest = 378 rs

Time = 2 year

Rate = Simple interest × 100

principal × time

= 378 × 100

1800 × 2

= 10.5 %

Answer 2

The rate of interests is 10%.

Explanation:

The formula to find the compound interest :

$CI=P((1+r)^t-1)$ , where P=Principal , t= time , r= rate of interest.

As per given , we have

P= 1800

CI =378

t=2

Put all values in above formula , we get

$378= 1800((1+r)^2-1)\\\\ \dfrac{378}{1800}=(1+r^2+2r-1)\ \ [(a+b)^2=a^2+b^2+2ab]\\\\ 0.21 = r^2+2r\\\\ r^2+2r-0.21=0\\\\ r^2+2.1r-0.1r-0.21=0\\\\ (r+2.1)(r-0.1)=0\\\\ r=-2.1 , 0.1$

Since r cannot be negative ( because r is rate of growth not decay here) , so r= 0.1

In percent  , r= 0.1 x 100 = 10%

Hence, the rate of interests is 10%.

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Find compund interest if principal is 2000 , rate of interest is 5% pa and time is 3years

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