A person invests $2000 at a rate of 5% per annum compounded annually. What will

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Question: A person invests $2000 at a rate of 5% per annum compounded annually. What will be the amount after 3 years?

Options:

Correct Answer: $2315.25

Solution:

Amount = P(1 + r/n)^(nt) = 2000(1 + 0.05/1)^(1*3) = 2000(1.157625) = $2315.25.

A person invests $2000 at a rate of 5% per annum compounded annually. What will be the amount after 3 years?

A person invests $2000 at a rate of 5% per annum compounded annually. What will be the amount after 3 years?

Step 1: Identify the initial investment amount (P), which is $2000.
Step 2: Identify the annual interest rate (r), which is 5% or 0.05 in decimal form.
Step 3: Identify the number of times the interest is compounded per year (n), which is 1 since it is compounded annually.
Step 4: Identify the number of years the money is invested (t), which is 3 years.
Step 5: Use the formula for compound interest: Amount = P(1 + r/n)^(nt).
Step 6: Substitute the values into the formula: Amount = 2000(1 + 0.05/1)^(1*3).
Step 7: Simplify the expression inside the parentheses: 1 + 0.05 = 1.05.
Step 8: Calculate the exponent: 1*3 = 3, so we have Amount = 2000(1.05)^3.
Step 9: Calculate (1.05)^3, which equals approximately 1.157625.
Step 10: Multiply the initial investment by this result: Amount = 2000 * 1.157625.
Step 11: Calculate the final amount: 2000 * 1.157625 = $2315.25.

Compound Interest – Understanding how to calculate the future value of an investment using the formula for compound interest.
Investment Calculation – Applying the principles of finance to determine the total amount after a specified period.