Calculating Principal Amount Using CI and SI Difference
This problem requires finding the principal amount (P) when the difference between compound interest (CI) and simple interest (SI) for a period of 2 years is given, along with the annual interest rate (R).
Formula for Difference Between CI and SI (2 Years)
The specific formula relating the difference between CI and SI for 2 years to the principal (P) and rate (R) is:
Difference = $ P \times \left(\frac{R}{100}\right)^2 $
Applying the Formula
We are given:
- Difference = Rs. 205
- Rate (R) = 5% p.a.
- Time = 2 years
Substitute these values into the formula:
$ 205 = P \times \left(\frac{5}{100}\right)^2 $
Step-by-Step Calculation
- Simplify the rate term: $ \frac{5}{100} = \frac{1}{20} $
- Square the simplified rate term: $ \left(\frac{1}{20}\right)^2 = \frac{1}{400} $
- Rewrite the equation: $ 205 = P \times \frac{1}{400} $
- Solve for P by multiplying both sides by 400: $ P = 205 \times 400 $
- Calculate the final amount: $ P = 82000 $
Therefore, the amount invested is Rs. 82,000.
Important Questions from Simple and Compound Both
What is the compound interest (in Rs.) at the rate of 10%, compounded annually, for 3 years on the principal which in 8 years at the rate of 12% per annum gives Rs. 4,800 as simple interest?
A certain sum amounts to Rs. 15,500 in 2 years at 12% p.a. simple interest. If the same sum is compounded half-yearly at 10% per annum for \(1 \frac{1}{2}\) years, what will be the amount received?
The difference in compound interest on a certain sum at 10% p.a. for one year, when the interest is compounded half-yearly and yearly, is Rs. 88.80. What is the simple interest on the same sum for \(1\frac{2}{3}\) years at the same rate?
A sum of Rs. 7500 amounts to Rs. 9075 at 10% p.a, interest being compounded yearly in a certain time. The simple interest (in Rs.) on the same sum for the same time and the same rate is:
A certain sum amounts to Rs.291600 in 2 years and to Rs.314928 in 3 years on compound interest compounded annually. How much will be the simple interest (in Rs.) on Rs.40000 at the same rate for 2 years?
