the difference between simple interest and compound interest for 2 year at 4% per annum is ₹20 the principal (in ₹) will be
Answers
Step-by-step explanation:
Given :-
The difference between simple interest and compound interest for 2 year at 4% per annum is ₹20 .
To find :-
Find the principal (in ₹) ?
Solution:-
Method -1:-
Let the principle be ₹ X
Time = 2 years
Rate of Interest = 4%
We know that
Simple Interest = PTR/100
=> SI = (X×2×4)/100
=> SI = 8X/100
=> SI = 2X/25
Simple Interest = ₹ 2X/25 -------------(1)
We know that
Compound Amount = P[1+(R/100)]^n]
Amount = Principle+Interest
=> Compound Interest = Amount-Principle
=> C.I = P[1+(R/100)]^n-P
=>CI = P[ [1+(R/100)]^n -1]
=>CI = X[[ 1+(4/100)]^2-1]
=> CI =X[[1+(1/25)]^2-1]
=> CI = X[(25+1)/25)^2-1]
=> CI = X[(26)/25)^2-1]
=> CI = X[(676/625)-1]
=> CI = X[(676-625)/625]
=> CI = 51X/625
Compound Interest = ₹ 51X/625 -------(2)
Given that
The difference between CI and SI = ₹20
=> (51X/625) - (2X/25) = 20
=> (51X-50X)/625 = 20
=> X/625 = 20
=> X = 20×625
=> X = ₹12500
=> P = ₹12500
Short -cut:-
The difference between the CI and SI is D, Rate of Interest R % and time is 2 Years then
D = P(R/100)^2
We have
D = ₹20 , R = 4%
=> 20 = P(4/100)^2
=> 20 = P(1/25)^2
=> 20 = P(1/625)
=> 20 = P/625
=> P = 20×625
=> P = ₹12500
Answer :-
The principle for the given problem is ₹12500
Used formulae:-
- Simple Interest = PTR/100
- Compound Amount = P[1+(R/100)]^n]
- Amount = Principle+Interest
- C.I = P[1+(R/100)]^n-P
- The difference between the CI and SI is D, Rate of Interest R % and time is 2 Years then D = P(R/100)^2