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