Find Invested Amount from Interest Difference
This problem requires calculating the principal amount (the initial investment) based on the difference between compound interest (CI) and simple interest (SI) earned over two years.
Compound vs Simple Interest Formula for 2 Years
The difference between compound interest and simple interest for a principal amount 'P' invested for 2 years at a rate 'r' (in decimal form) is given by the formula:
Difference = $P \times r^2$
We are given:
- Difference = Rs. 470
- Rate (r) = 10% p.a. = $\frac{10}{100}$ = 0.10
- Time = 2 years
Now, we substitute the known values into the formula:
$470 = P \times (0.10)^2$
Calculate the square of the rate:
$470 = P \times 0.01$
To find the principal amount (P), rearrange the equation:
$P = \frac{470}{0.01}$
Perform the division:
$P = 470 \times 100$
$P = 47000$
Therefore, the amount invested is Rs. 47000.
Important Questions from Simple and Compound Both
- 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.)
- 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.)
