What is the difference between the compound interest and simple interest on a su

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Question: What is the difference between the compound interest and simple interest on a sum of $1000 at 5% per annum after 2 years? (2023)

Options:

Correct Answer: $20

Exam Year: 2023

Solution:

SI = 1000 * 5 * 2 / 100 = $100. CI = 1000[(1 + 0.05)^2 - 1] = $102.5. The difference is $2.5.

What is the difference between the compound interest and simple interest on a sum of $1000 at 5% per annum after 2 years? (2023)

What is the difference between the compound interest and simple interest on a sum of $1000 at 5% per annum after 2 years? (2023)

Step 1: Identify the principal amount, which is $1000.
Step 2: Identify the interest rate, which is 5% per annum.
Step 3: Identify the time period, which is 2 years.
Step 4: Calculate Simple Interest (SI) using the formula: SI = Principal * Rate * Time / 100.
Step 5: Substitute the values into the formula: SI = 1000 * 5 * 2 / 100.
Step 6: Calculate SI: SI = 1000 * 5 * 2 / 100 = $100.
Step 7: Calculate Compound Interest (CI) using the formula: CI = Principal * (1 + Rate)^Time - Principal.
Step 8: Convert the interest rate to decimal: 5% = 0.05.
Step 9: Substitute the values into the CI formula: CI = 1000 * (1 + 0.05)^2 - 1000.
Step 10: Calculate (1 + 0.05)^2 = 1.1025.
Step 11: Substitute this value into the CI formula: CI = 1000 * 1.1025 - 1000.
Step 12: Calculate CI: CI = 1102.5 - 1000 = $102.5.
Step 13: Find the difference between CI and SI: Difference = CI - SI.
Step 14: Substitute the values: Difference = 102.5 - 100.
Step 15: Calculate the difference: Difference = $2.5.

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