Understanding the Interest Difference
The problem asks for the principal amount (P) invested equally in simple interest (SI) and compound interest (CI) under specific conditions.
- Time period (T) = 2 years
- Rate of interest (R) = 4% per annum
- Interest is compounded annually.
- Difference between CI and SI = ₹53
Calculating Principal Amount
For a time period of 2 years, the difference between compound interest (CI) and simple interest (SI) is given by the formula:
Difference = $ \frac{P \times R^2}{10000} $
Where:
- P is the principal amount
- R is the annual rate of interest in percent
Substitute the given values into the formula:
₹53 = $ \frac{P \times (4)^2}{10000} $
₹53 = $ \frac{P \times 16}{10000} $
Now, solve for P:
$ P = \frac{₹53 \times 10000}{16} $
$ P = \frac{530000}{16} $
$ P = 33125 $
Investment Amount
The principal amount invested in each case (Simple Interest and Compound Interest) was ₹33,125.
Important Questions from Simple and Compound Intrest
The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. The rate of interest per annum is?
A sum of Rs. 2000 amounts to Rs. 4000 in two years at compound interest. In how many years does the same amount becomes Rs. 8000?
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, the compound interest on the same at the same rate and for the same time is:
- Amit invested the same sum at simple and compound interest (compounded annually) for 2 years at 4% per annum. The difference between the compound interest and the simple interest is ₹47. Find the sum (in ₹) invested in each case.
- The simple interest on a certain sum for $2\frac{6}{7}$ years at the rate of 7.7% per annum is ₹1,188.
What will be the amount payable on the same sum at the rate of 8.5% per annum simple interest in $4\frac{5}{9}$ years?
