What is the compound interest on $8000 at a rate of 5% per annum for 2 years?
Practice Questions
Q1
What is the compound interest on $8000 at a rate of 5% per annum for 2 years?
$800.00
$850.00
$820.00
$900.00
Questions & Step-by-Step Solutions
What is the compound interest on $8000 at a rate of 5% per annum for 2 years?
Correct Answer: 820.00
Step 1: Identify the principal amount (P), which is $8000.
Step 2: Identify the annual interest rate (r), which is 5% or 0.05 in decimal form.
Step 3: Identify the number of years (t), which is 2 years.
Step 4: Use the compound interest formula: A = P(1 + r)^t, where A is the total amount after interest.
Step 5: Substitute the values into the formula: A = 8000(1 + 0.05)^2.
Step 6: Calculate (1 + 0.05) = 1.05.
Step 7: Raise 1.05 to the power of 2: (1.05)^2 = 1.1025.
Step 8: Multiply this result by the principal: A = 8000 * 1.1025 = 8820.
Step 9: Calculate the compound interest by subtracting the principal from the total amount: Compound Interest = A - P = 8820 - 8000.
Step 10: The compound interest is $820.
Compound Interest – The interest calculated on the initial principal, which also includes all the accumulated interest from previous periods on a deposit or loan.
Exponential Growth – Understanding how the interest compounds over time, leading to growth that accelerates as time progresses.
Percentage Calculation – Applying the percentage rate to the principal amount to determine the interest earned.
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