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
- 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).
- The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 10% per annum is $₹407$. Find the sum [rounded off to the nearest integer].
The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 17% per annum is ₹967. Find the sum [rounded off to the nearest integer].
- 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 ₹186 at 10% interest per annum, the principal is ₹______.
