Question

The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2 years is Rs. 56. Find the sum.​

Answer 1

Step-by-step explanation:

Given :-

The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2 years is Rs. 56.

To find:-

Find the sum ?

Solution :-

General Method :-

Given that :

The difference between the compound interest and simple interest (d) = Rs. 56

Rate of interest (R)= 10%

Time (T) = 2 years

Let the principle be Rs. X

Finding Simple Interest :-

We know that

Simple Interest (S.I) = PTR/100

=> S.I = (X×2×10)/100

=> S.I =20X/100

=> S.I = X/5

Simple Interest = Rs. X/5 ---------(1)

Finding Compound Interest:-

We know that

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

=> A = X[1+(10/100)]²

=> A = X[1+(1/10)]²

=> A = X[(10+1)/10]²

=> A = X(11/10)²

=> A = X(121/100)

=> A = 121X/100

Amount = Rs. 121X/100

We know that

Amount = Principle + Interest

=> Interest = Amount - Principle

=> Interest = (121X/100)-X

=> Interest = (121X-100X)/100

=> Interest = 21X/100

Compound Interest = Rs. 21X/100--------(2)

On Subtracting (1) from (2) then

=> Difference = (21X/100)-(X/5)

=> d = (21X-20X)/100

=> d = X/100

The difference between C.I and S.I = Rs. X/100

According to the given problem

Difference = Rs. 56

=> X/100 = 56

=>X = 56×100

=> X = 5600

The sum = Rs. 5600

Shortcut :-

The difference between the CI and SI for 2 years is D ,Rate of Interest is R % and Principle is P then

D = P(R/100)²

We have

D = Rs. 56

P = RS. X

R = 10%

On Substituting these values in the above formula

=> 56 = X(10/100)²

=> 56 = X (1/10)²

=>56 = X/100

=>X/100 = 56

=> X = 56×100

=> X = 5600

The sum = Rs. 5600

Answer:-

The Principle for the given problem is Rs. 56000

Used formulae:-

• Simple Interest (S.I) = PTR/100

• Amount = Principle + Interest

• Amount (A) = P[1+(R/100)]^n

• The difference between the CI and SI for 2 years is d ,Rate of Interest is R % and Principle is P then D = P(R/100)²

Where,

• P = Principle
• T = Time
• R = Rate of Interest
• A = Amount
• n= Number of times the compound interest is calculated
• D = Difference