This question asks us to find the difference between the compound interest (CI) and simple interest (SI) earned on a principal amount of ₹17,700 at an annual interest rate of 4% for a period of 2 years.
Calculating Simple Interest (SI)
Simple interest is calculated only on the principal amount. The formula for SI is:
$$ \text{SI} = \frac{P \times R \times T}{100} $$Where:
- P = Principal amount = ₹17,700
- R = Rate of interest per annum = 4%
- T = Time period in years = 2 years
Plugging in the values:
$$ \text{SI} = \frac{17700 \times 4 \times 2}{100} $$ $$ \text{SI} = 177 \times 4 \times 2 $$ $$ \text{SI} = 177 \times 8 $$ $$ \text{SI} = 1416 $$So, the Simple Interest is ₹1,416.
Calculating Compound Interest (CI)
Compound interest is calculated on the principal amount plus the accumulated interest from previous periods. The formula for CI is:
$$ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P $$Using the same values:
$$ \text{CI} = 17700 \left(1 + \frac{4}{100}\right)^2 - 17700 $$ $$ \text{CI} = 17700 \left(1 + 0.04\right)^2 - 17700 $$ $$ \text{CI} = 17700 \left(1.04\right)^2 - 17700 $$First, calculate $ (1.04)^2 $:
$$ (1.04)^2 = 1.0816 $$Now, substitute this back into the CI formula:
$$ \text{CI} = 17700 \times 1.0816 - 17700 $$ $$ \text{CI} = 19144.32 - 17700 $$ $$ \text{CI} = 1444.32 $$So, the Compound Interest is ₹1,444.32.
Finding the Difference
The difference between compound interest and simple interest is:
$$ \text{Difference} = \text{CI} - \text{SI} $$ $$ \text{Difference} = 1444.32 - 1416 $$ $$ \text{Difference} = 28.32 $$Shortcut for 2-Year Difference
For a time period of 2 years, there's a direct formula to calculate the difference between CI and SI:
$$ \text{Difference} = P \left(\frac{R}{100}\right)^2 $$Using the given values:
$$ \text{Difference} = 17700 \left(\frac{4}{100}\right)^2 $$ $$ \text{Difference} = 17700 \left(0.04\right)^2 $$ $$ \text{Difference} = 17700 \times 0.0016 $$ $$ \text{Difference} = 28.32 $$Both methods yield the same result. The difference between the compound interest and the simple interest is ₹28.32.
Important Questions from Simple and Compound Intrest
Amit had invested same amount of sums at simple as well as compound interest, compounded annually. The time period of investment for both the sums was 2 years and rate of interest too was the same, 4% per annum. At the end, he found a difference of ₹43 in both the interests received. What were the sums (in ₹) invested?
When the difference between compound interest, compounded annually, and simple interest for three years is ₹186 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹217 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹228 at 4% interest per annum, the principal is ₹______.
- The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 16% per annum is ₹797. Find the sum (rounded off to the nearest integer).
