The simple interest on a certain sum for 3 years
is Ray 1080 and the the compound interest at the same sum same rate for 2 years is RS 74160. find
i The rate of interest
¿ The principal
Answers
Step-by-step explanation:
Given :-
The simple interest on a certain sum for 3 years
is Rs. 1080 and the the compound interest at the same sum same rate for 2 years is Rs. 741.60
Correction :-
Rs. 741.60
To find :-
Find the following:
i) The rate of interest
ii) The principal
Solution :-
Let the principle be Rs. X
Let the Rate of Interest be R%
Simple interest on it = Rs. 1080
Time = 3 years
We know that
Simple Interest = PTR/100
On Substituting these values in the above formula then
=> 1080 = (X×3×R)/100
=> 1080 = 3RX/100
=> 3RX/100 = 1080
=> 3RX = 1080×100
=> 3RX = 108000
=> RX = 108000/3
=> RX = 36000
=> X = Rs. 36000/R ----------------(1)
and Given that
Compound interest = Rs. 741.60
Principle = Rs. X
Rate of Interest = R%
Time = 2 years
Number of times the Compound Interest is calculated per 2 years = 2
n = 2
We know that
A = P[1+(R/100)]^n
On Substituting these values in the above formula then
=> A = X[1+(R/100)]²
=> A = X[(100+R)/100]²
Amount = Principle + Interest
=> X[(100+R)/100]² = X + 741.60
=> X[(100+R)/100]²-X = 741.60
=> X[{(100+R)/100}²-1] = 741.60
=> X[{(100+R)²/10000}-1] = 741.60
=> X[{(100+R)²-10000}/10000] = 741.60
=> X[(10000+R²+200R-10000)/10000] = 741.60
=> X[(R²+200R)/10000] = 741.60
From (1)
=> (36000/R)[(R²+200R)/10000] = 741.60
=> (36000/10000)[(R²+200R)/R ]=741.60
=> (18/5)[R(R+200)/R] = 741.60
=> (18/5)(R+200) = 741.60
=> (18)(R+200) = 741.60×5
=> 18(R+200) = 3708
=> R+200 = 3708/18
=> R+200 = 206
=> R = 206-200
=> R = 6 %
So ,Rate of Interest = 6%
Now
On Substituting the value of R in (1)
X = 36000/6
=> X = 6000
So, Principle = Rs. 6000
Answer :-
I) Rate of Interest for the given problem is 6%
II) Principle for the given problem is Rs. 6000
Check:-
P = Rs. 6000
T = 3 years
R = 6%
SI = (6000×3×6)/100
=> SI = 60×3×6
=> SI = Rs.1080
Time = 2 years
A = 6000[1+(6/100)]²
=> A = 6000[1+(3/50)]²
=> A = 6000(53)/50)²
=> A = (6000×53×53)/2500
=> A = (60×53×53)/25
=> A= 12×53×53/5
=> A = 33708/5
=>A = Rs. 6741.60
CI = A-P
=> CI = 6841.60-6000
=> CI = Rs. 741.60
Verified the given relations in the given problem.
Used formulae:-
- Simple Interest = PTR/100
- A = P[1+(R/100)]^n
- Amount = Principle + Interest
- T = Time
- n = Number of times the Compound Interest is calculated
- SI = Simple Interest
- CI = Compound Interest