Question

The simple interest is Rs.1 less than the compound interest on a certain principal for a period of 2 years at 10% interest. Find the principal..
1. Rs. 100
2. Rs. 110
3. Rs. 95
4. Rs. 90

Answer 1

Correct Answer - Option 1 : Rs. 100

Given:

The simple interest is Rs.1 less than the compound interest on a certain principal for a period of 2 years at 10% interest.

Time = 2 years

Rate of interest = 10%

Formula used:

C.I = P[(1 + (R/100))^T – 1]

S.I = (P × R × T)/100

Where,

C.I → Compound Interest 

S.I → Simple Interest

P → Principal

R → Rate of interest

T → Time

Calculation:

C.I = P[(1 + (R/100))T – 1]

⇒ C.I = P[(1 + (10/100))² – 1]

⇒ P[(121/100) – 1]

⇒ (21P/100)

S.I = (P × R × T)/100

⇒ S.I = (P × 10 × 2)/100

⇒ (20P)/100

C.I – S.I = 1

⇒ (21P/100) –  (20P/100) = 1

⇒ P/100 = 1

⇒ P = 100

∴ The principal is Rs. 100.