If a person invests $5000 at a compound interest rate of 4% per annum, how much

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Question: If a person invests $5000 at a compound interest rate of 4% per annum, how much will he have after 3 years?

Options:

Correct Answer: $5624.64

Solution:

Amount = P(1 + r)^t = 5000(1 + 0.04)^3 = 5000(1.124864) = $5624.64.

If a person invests $5000 at a compound interest rate of 4% per annum, how much will he have after 3 years?

If a person invests $5000 at a compound interest rate of 4% per annum, how much will he have after 3 years?

Step 1: Identify the initial investment amount (P), which is $5000.
Step 2: Identify the annual interest rate (r), which is 4%. Convert this to decimal form by dividing by 100, so r = 0.04.
Step 3: Identify the number of years the money is invested (t), which is 3 years.
Step 4: Use the compound interest formula: Amount = P(1 + r)^t.
Step 5: Substitute the values into the formula: Amount = 5000(1 + 0.04)^3.
Step 6: Calculate (1 + 0.04) = 1.04.
Step 7: Raise 1.04 to the power of 3: (1.04)^3 = 1.124864.
Step 8: Multiply this result by the initial investment: Amount = 5000 * 1.124864.
Step 9: Calculate the final amount: 5000 * 1.124864 = $5624.64.

Compound Interest – The process of earning interest on both the initial principal and the accumulated interest from previous periods.
Formula Application – Using the formula A = P(1 + r)^t to calculate the future value of an investment.
Exponential Growth – Understanding how compound interest leads to exponential growth of an investment over time.