If the difference between the compound interest and simple interest on a certain sum of money for 2 years at 10% is $50, what is the principal? (2000)
Practice Questions
1 question
Q1
If the difference between the compound interest and simple interest on a certain sum of money for 2 years at 10% is $50, what is the principal? (2000)
$1000
$1200
$1500
$2000
The difference between CI and SI for 2 years is given by P * (r^2)/100^2. Setting this equal to $50 and solving gives P = $1500.
Questions & Step-by-step Solutions
1 item
Q
Q: If the difference between the compound interest and simple interest on a certain sum of money for 2 years at 10% is $50, what is the principal? (2000)
Solution: The difference between CI and SI for 2 years is given by P * (r^2)/100^2. Setting this equal to $50 and solving gives P = $1500.
Steps: 8
Step 1: Understand the problem. We need to find the principal amount (P) where the difference between compound interest (CI) and simple interest (SI) for 2 years at a rate of 10% is $50.
Step 2: Recall the formula for the difference between CI and SI for 2 years: Difference = P * (r^2) / (100^2), where r is the rate of interest.
Step 3: Substitute the values into the formula. Here, r = 10%, so we have: Difference = P * (10^2) / (100^2).
Step 4: Simplify the formula. 10^2 = 100, and 100^2 = 10000, so the formula becomes: Difference = P * (100) / (10000).
Step 5: This simplifies to: Difference = P / 100.
Step 6: We know the difference is $50, so we set up the equation: P / 100 = 50.
Step 7: To find P, multiply both sides of the equation by 100: P = 50 * 100.
