Question

The difference between compound interest and simple interest at 10 % per annum in two years is Rs 50. Find the sum.​

Answer 1

Given that:

• The difference between compound interest and simple interest at 10 % per annum in two years is Rs 50.

To Find:

• The sum of money/Principal.

Let us assume:

• The sum of money be P.

• Rate of interest = 10% p.a.
• Time period = 2 years

We know that:

• C.I. = P(1 + R/100)ᵀ - P
• S.I. = PRT/100

where,

• C.I. = Compound interest
• S.I. = Simple interest
• P = Sum of money
• R = Rate of interest
• T = Time period

According to the question:

C.I. - S.I. = 50

P(1 + R/100)ᵀ - P - PRT/100 = 50

Putting all the values.

ㅤ↠ㅤP(1 + 10/100)² - P - (P × 10 × 2)/100 = 50

ㅤ↠ㅤP(1 + 0.1)² - P - (20P)/100 = 50

ㅤ↠ㅤP(1.1)² - P - 0.2P = 50

ㅤ↠ㅤP(1.21) - P - 0.2P = 50

Taking P common in L.H.S.

ㅤ↠ㅤP(1.21 - 1 - 0.2) = 50

ㅤ↠ㅤP(0.01) = 50

ㅤ↠ㅤP = 50/0.01

ㅤ↠ㅤP = (50 × 100)/1

ㅤ↠ㅤP = 5000

Hence,

• The sum of money is Rs. 5000.