If the difference between the compound interest and simple interest on a certain
Practice Questions
Q1
If the difference between the compound interest and simple interest on a certain sum of money for 2 years at 10% per annum is $50, what is the principal? (2000)
$1000
$1200
$1500
$2000
Questions & Step-by-Step Solutions
If the difference between the compound interest and simple interest on a certain sum of money for 2 years at 10% per annum is $50, what is the principal? (2000)
Step 1: Understand that the difference between compound interest (CI) and simple interest (SI) for 2 years can be calculated using the formula: Difference = SI * (r/100)^2.
Step 2: Identify the values given in the problem. The rate (r) is 10%, and the difference is $50.
Step 3: Write the formula with the known values: 50 = SI * (10/100)^2.
Step 4: Simplify the formula: (10/100) = 0.1, so (10/100)^2 = 0.1^2 = 0.01. Now the equation is: 50 = SI * 0.01.
Step 5: Solve for SI: SI = 50 / 0.01 = 5000.
Step 6: Use the formula for simple interest: SI = Principal * (rate/100) * time. Here, SI = 5000, rate = 10, and time = 2 years.
Step 7: Substitute the values into the formula: 5000 = Principal * (10/100) * 2.
Step 8: Simplify the equation: 5000 = Principal * 0.2.
Step 9: Solve for Principal: Principal = 5000 / 0.2 = 25000.
Step 10: Verify the calculations to ensure the principal is correct.
Compound Interest vs. Simple Interest – Understanding the difference between compound interest and simple interest, particularly how they accumulate over time.
Interest Calculation – Applying the formulas for calculating simple interest and compound interest over a specified period.
Algebraic Manipulation – Solving equations to find the principal amount based on the given difference in interest types.
