What is the difference between simple interest and compound interest on Rs 10 00...........

Quantitative Aptitude (CDS) Compound Interest

What is the difference between simple interest and compound interest on Rs. 10,000 for two years at 20% per annum compounded half-yearly ?

This questions was previously asked in

2023 CDS -1 MATH

View All CDS Previous Year Papers

Rs.842

Rs.756

Rs.641

Rs.542

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Explanation:

- Simple Interest is calculated on the original principal throughout the period. For Rs. 10,000 at 20% p.a. for 2 years, Simple Interest (SI) = P * R * T / 100 = 10,000 * 20 * 2 / 100 = Rs. 4,000.

- Compound Interest involves interest on the principal and accumulated interest. Here, it's compounded half-yearly. So, n = 2 times per year. Use the formula CI = P * (1 + (R/2)/100)^(n*T) - P.

- Principal (P) = Rs. 10,000, Rate (R) = 20% p.a.

- Half-yearly rate = 10%, Time (n*T) = 4 periods (2 years).

- CI = 10,000 * (1 + 10/100)^4 - 10,000 = 10,000 * (1.1)^4 - 10,000 = 10,000 * 1.4641 - 10,000 = Rs. 4,641.

- Difference between CI and SI = Rs. 4,641 - Rs. 4,000 = Rs. 641.

- Option 3: Rs. 641 is correct.