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
- The difference between the interest earned on the same amount invested under compound interest and simple interest at same rate of interest for 2 years is Rs.470. If the rate of interest is 10% p.a. then find the amount invested? (In Rs.)
- Suresh lent a sum of money on compound interest in such a way that it amounted to three times in 4 years. For how much time should he invest his money so that he gets back an amount which is 9 times of the sum of money lent by him?
The compound interest on a certain sum for 3 years at 8% per annum is Rs. 1,94,784. What is the simple interest on the $\frac{9}{10}$ part of the sum for the same time but at a rate of interest per annum which is $1\frac{1}{2}$ time the rate of interest per annum as applicable for compound interest?
- There is 60% increase in an amount in 4 years at simple interest. What will be the compound interest on Rs.49500 after 2 years at the same rate of interest? (In Rs.)
- The difference between the interest earned on the same amount invested under compound interest and simple interest at same rate of interest for 2 years is Rs.945. If the rate of interest is 15% p.a. then find the amount invested? (In Rs.)
