Calculate the compound interest on $5000 at 8% per annum for 3 years, compounded

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Question: Calculate the compound interest on $5000 at 8% per annum for 3 years, compounded annually.

Options:

Correct Answer: $1,400

Solution:

Compound Interest = 5000(1 + 0.08)^3 - 5000 = 5000(1.259712) - 5000 = $1298.56

Calculate the compound interest on $5000 at 8% per annum for 3 years, compounded annually.

Calculate the compound interest on $5000 at 8% per annum for 3 years, compounded annually.

Step 1: Identify the principal amount (P), which is $5000.
Step 2: Identify the annual interest rate (r), which is 8% or 0.08 in decimal form.
Step 3: Identify the number of years (t), which is 3 years.
Step 4: Use the compound interest formula: A = P(1 + r)^t, where A is the total amount after t years.
Step 5: Substitute the values into the formula: A = 5000(1 + 0.08)^3.
Step 6: Calculate (1 + 0.08) = 1.08.
Step 7: Raise 1.08 to the power of 3: (1.08)^3 = 1.259712.
Step 8: Multiply this result by the principal: A = 5000 * 1.259712.
Step 9: Calculate A = 6298.56.
Step 10: To find the compound interest, subtract the principal from the total amount: Compound Interest = A - P = 6298.56 - 5000.
Step 11: Calculate the compound interest: Compound Interest = 1298.56.

Compound Interest – The interest calculated on the initial principal, which also includes all the accumulated interest from previous periods.
Exponential Growth – Understanding how money grows over time when interest is compounded.
Formula Application – Applying the compound interest formula correctly: A = P(1 + r/n)^(nt).