1. Understand the problem: We need to find the principal amount (sum of money) given the difference between simple interest (SI) and compound interest (CI) for 2 years at 16% interest.
2. Formulas:
- Simple Interest (SI) = (P * R * T) / 100 where P = principal, R = rate, T = time
- Compound Interest (CI) = P(1 + R/100)T - P
3. Calculate SI and CI:
- Let P be the principal amount.
- SI for 2 years at 16% = (P * 16 * 2) / 100 = 0.32P
- CI for 2 years at 16% = P(1 + 16/100)² - P = P(1.16)² - P = 1.3456P - P = 0.3456P
4. Find the difference:
- The difference between CI and SI is given as ₹797.
- Therefore, 0.3456P - 0.32P = 797
- 0.0256P = 797
- P = 797 / 0.0256
- P ≈ 31132.8125
5. Round off:
- Rounding off to the nearest integer, we get P = ₹31133
6. Eliminate Incorrect Options: The options provided are close, highlighting the importance of accurate calculation. The other options are incorrect because they do not satisfy the equation 0.0256P = 797.
Therefore, the correct answer is ₹31,133.
Important Questions from Simple and Compound Intrest
Amit had invested same amount of sums at simple as well as compound interest, compounded annually. The time period of investment for both the sums was 2 years and rate of interest too was the same, 4% per annum. At the end, he found a difference of ₹43 in both the interests received. What were the sums (in ₹) invested?
When the difference between compound interest, compounded annually, and simple interest for three years is ₹186 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹217 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹228 at 4% interest per annum, the principal is ₹______.
- The difference between the compound interest, compounded annually and the simple interest if ₹17,700 is deposited at 4% rate of interest per annum for 2 years is:
