Question

The difference between simple and compound interest on a principal amount is Rs. 27 when rate of interest is 5% per annum and amount is kept for 2 years. Find the principal amount.
1. Rs. 18800
2. Rs. 10800
3. Rs. 12580
4. Rs. 25000

Answer 1

Correct Answer - Option 2 : Rs. 10800

Given:

C.I. – S.I. = Rs. 27

R = 5%

N = 2 years

Formula used:

In case of compound interest

A = P × {1 + (R / 100)}^N

Where P = Principal amount, R = Rate of interest in %, N = Number of years, A = Amount

In case of simple interest

I = PRN / 100

Where P = Principal amount, R = Rate of interest in %, N = Number of years, I = Interest earned

A = P + I

Calculation:

Here, C.I. – S.I. = 27

Also, C.I. = P × {1 + (R / 100)}^N – P

And S.I = PRN/100

Accordingly,

⇒ P × {1 + (R / 100)}N – P – (PRN / 100) = 27

⇒ P{(1 + R/100)^N - 1 - (RN/100)} = 27

⇒ P{(1 + 5/100)² - 1 - (5 × 2)/100} = 27

⇒ P × {441/400 - 1 - 1/10} = 27

⇒ P × (1/400) = 27

⇒ P = 27 × 400

⇒ P = 10800

∴ Principal amount is Rs. 10800.