If the difference between the simple interest and compound interest on the same principal at 4% per annum for 2 years is Rs.8, then the principal is (compound interest compounded annually)
1. Rs.4,500
2. Rs.5,000
3. Rs.5,100
4. None of the above
1. Rs.4,500
2. Rs.5,000
3. Rs.5,100
4. None of the above
Correct Answer – Option 2 : Rs.5,000
Given:
The difference between simple interest and compound interest on the principal = Rs. 8
Rate of interest = 4% p.a
Number of years = 2 years
Formula used:
SI = PTR/100
CI = P[(1 + r/100)n – 1]
Calculations:
Let principal be ‘p’
SI = p × 4 × 2/100
⇒ SI = 8p/100
CI = p[(1 + 4/100)2 – 1]
⇒ CI = p[(1 + 1/25)2 – 1]
⇒ CI = p[(26/25)2 – 1]
⇒ CI = p(1.0816 – 1)
⇒ CI = 0.0816p
Difference between SI and CI = 0.0816p – 0.08p
⇒ 0.0016p = 8
⇒ p = 8/0.016
⇒ p = 5000
∴ The Principal is Rs 5000