If the difference between the simple interest and compound interest on

1.	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.4,5002. Rs.5,0003. Rs.5,1004. None of the above
Answer» 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

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.4,5002. Rs.5,0003. Rs.5,1004. None of the above

Answer» 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

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