Question

the compound interest on Rs 200 for 2 years is Rs 42. Find rate of interest. ​

Answer 1

Step-by-step explanation:

Given :-

The compound interest on Rs 200 for 2 years is Rs 42.

To find :-

Find rate of interest?

Solution :-

Given that :

The compound interest =Rs. 42

Principle = Rs. 200

Time = 2 years

We know that

Amount = Principle + Interest

=> Amount = 200+42

=> Amount = Rs. 242

Let the rate of interest be R%

We know that

The Amount A = P[1+(R/100)]^n

Where n = 2, P = Rs.200 , A = Rs.242

On Substituting these values in the above formula then

=> 242 = 200[1+(R/100)]^2

=> 242/200 = [1+(R/100)]^2

=> 121/100 = [1+(R/100)]^2

=> [1+(R/100)]^2 = 121/100

=> 1+(R/100) = √(121/100)

=> 1+(R/100) = 11/10

=> R/100 = (11/10)-1

=> R/100 = (11-10)/10

=> R/100 = 1/10

=> R = (1/10)×100

=> R = 100/10

=> R = 10

Therefore , R = 10%

Answer:-

The Rate of Interest for the given problem is 10%

Check :-

We have , P = Rs. 200, R = 10% , n = 2

A = P[1+(R/100)]^n

=> A= 200[1+(10/100)]^2

=>A= 200[1+(1/10)]^2

=> A = 200[(10+1)/10]^2

=>A = 200(11/10)^2

=> A = (200×11×11)/(10×10)

=> A = 24200/100

=> A = 242

Amount = Rs. 242

Compound Interest = Amount - Principle

=> CI = 242-200

=> Compound Interest =Rs. 42

Verified the given relations in the given problem

Used formulae:-

• Amount (A) = P[1+(R/100)]^n

Where,

• A = Amount

• P = Principle

• R = Rate of Interest

• n = Number of time the compound interest is calculated

• Amount = Principle+ Interest