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
- 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:
- The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 10% per annum is $₹407$. Find the sum [rounded off to the nearest integer].
The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 17% per annum is ₹967. Find the sum [rounded off to the nearest integer].
- 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 ₹186 at 10% interest per annum, the principal is ₹______.
