The problem requires finding the principal amount (P) invested, given the difference between compound interest (CI) and simple interest (SI) over 2 years.
Calculating Principal from Interest Difference
We are given:
- Difference between CI and SI for 2 years = Rs. 945
- Rate of interest (R) = 15% per annum
- Time period (T) = 2 years
The formula for the difference between compound interest and simple interest for 2 years is:
$ \text{Difference} = P \times \left(\frac{R}{100}\right)^2 $
Substitute the given values into the formula:
$ 945 = P \times \left(\frac{15}{100}\right)^2 $
Simplify the rate fraction:
$ \frac{15}{100} = \frac{3}{20} $
Now, calculate the square of the fraction:
$ \left(\frac{3}{20}\right)^2 = \frac{9}{400} $
The equation becomes:
$ 945 = P \times \frac{9}{400} $
To find the principal amount (P), rearrange the equation:
$ P = 945 \times \frac{400}{9} $
Calculate the value of P:
$ P = \frac{945}{9} \times 400 $
$ P = 105 \times 400 $
$ P = 42000 $
Therefore, the amount invested was Rs. 42,000.
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.205. If the rate of interest is 5% p.a. then find the amount invested? (In Rs.)
