Find the principal if the difference between C.I and S.I on it at 15% per annum for 3 years is ₹1134
Answers
Step-by-step explanation:
Given :-
The difference between C.I and S.I on it at 15% per annum for 3 years is ₹ 1134
To find :-
Find the Principle ?
Solution :-
General Method :-
Let the principle be ₹ X
Rate of Interest (R) = 15%
Time (T) = 3 years
We know that
Simple Interest (S.I) = PTR/100
=> S.I = (X×3×15)/100
=> S.I = 45X/100
=> S.I = 9X/20
Simple Interest = ₹ 9X/20
And
Compound Interest = P[{1+(R/100)^n} - 1]
=> C.I = X[{1+(15/100)}³ - 1]
=> C.I = X[1+(3/20)}³-1]
=> C.I = X[{(20+3)/20}³-1]
=> C.I = X[(23/20)³-1]
=> C.I = X[ (23×23×23/20×20×20)-1]
=> C.I = X [(12167/8000)-1]
=> C.I = X [ (12167-8000)/8000]
=> C.I = X[ 4167/8000]
=> C.I = 4167X/8000
Compound Interest = 4167X/8000
The difference between C.I and S.I
= (4167X/8000)-(9X/20)
LCM of 8000 and 20 is 8000
=> (4167X-3600X)/8000
=> 567X/8000
The difference = ₹ 567X/8000
According to the given problem
The difference between the C.I and S.I = ₹ 1134
=> 567X/8000 = 1134
=> 567X = 1134×8000
=> X = 1134×8000/567
=> X = 2×8000
=> X = 16000
Therefore, X = ₹ 16000
Shortcut :-
We know that
If the principle is P, Rate of Interest R , and the difference between the C.I and S.I for 3 years is
D =P(R/100)²[(R/100)+3]
We have
D = ₹ 1134
R = 15%
on Substituting these values in the above formula
=> 1134 = P(15/100)²[(15/100)+3]
=> 1134 = P(3/20)²[(3/20)+3]
=> 1134 = P(9/400)(3+60)/20
=> 1134 = P(9/400)(63/20)
=> 1134 = P(9×63)/(400×20)
=> 1134 = P(567)/8000
=> 1134 = 567P/8000
=> P = (1134×8000)/567
=> P = 2×8000
=> P = ₹ 16000
Answer:-
Principle for the given problem is ₹ 16000
Used formulae:-
- Simple Interest = PTR/100
- Compound Interest =P[{1+(R/100)^n} - 1]
- Amount = p[1+(R/100)]^n
- A = Amount
- P = Principle
- T = Time
- n = Number of times the interest calculated
- R = Rate of Interest
- If the principle is P, Rate of Interest R , and the difference between the C.I and S.I for 3 years isD =P(R/100)²[(R/100)+3]