The difference between simple and compound interest on a principal amo

1.	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. 188002. Rs. 108003. Rs. 125804. Rs. 25000
Answer» 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.

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. 188002. Rs. 108003. Rs. 125804. Rs. 25000

Answer» 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.