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What is the difference (in Rs) in Compound interest earned in 1 year on a sum of Rs. 25,000 at 20% per annum compounded semi-annually and annually?
- A125
- B250
- C500
- D375
Answer not set
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CCommunity
For annually, principal (P) = Rs. 25000, rate (R) = 20% and time (T) = 1 year
For semi-annually, principal (P) = Rs. 25000, semi-annually rate (R) = 20%/2 = 10%
And time (T) for semi-annually = 1 × 2 = 2 half year
Compound interest (CI, annually) = 25000(1 + 20/100) - 25000
⇒ CI (annually) = Rs. 5000
And Compound interest (CI, semi-annually) = 25000(1 + 10/100)2 - 25000
⇒ CI (semi-annually) = (25000 × 11/10 × 11/10) - 25000
⇒ CI (semi-annually) = Rs. 5250
∴ The difference between Compound interest earned in 1 year = 5000 - 5250 = Rs. 250
For semi-annually, principal (P) = Rs. 25000, semi-annually rate (R) = 20%/2 = 10%
And time (T) for semi-annually = 1 × 2 = 2 half year
Compound interest (CI, annually) = 25000(1 + 20/100) - 25000
⇒ CI (annually) = Rs. 5000
And Compound interest (CI, semi-annually) = 25000(1 + 10/100)2 - 25000
⇒ CI (semi-annually) = (25000 × 11/10 × 11/10) - 25000
⇒ CI (semi-annually) = Rs. 5250
∴ The difference between Compound interest earned in 1 year = 5000 - 5250 = Rs. 250