A person invests $1000 at a rate of 5% per annum compounded annually. What will

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Question: A person invests $1000 at a rate of 5% per annum compounded annually. What will be the amount after 2 years?

Options:

Correct Answer: $1100

Solution:

Amount = Principal * (1 + Rate)^Time = 1000 * (1 + 0.05)^2 = 1000 * 1.1025 = $1102.50.

A person invests $1000 at a rate of 5% per annum compounded annually. What will be the amount after 2 years?

A person invests $1000 at a rate of 5% per annum compounded annually. What will be the amount after 2 years?

Step 1: Identify the principal amount, which is the initial investment. In this case, it is $1000.
Step 2: Identify the annual interest rate. Here, it is 5%, which can be written as 0.05 in decimal form.
Step 3: Identify the time period for the investment. In this case, it is 2 years.
Step 4: Use the formula for compound interest: Amount = Principal * (1 + Rate)^Time.
Step 5: Substitute the values into the formula: Amount = 1000 * (1 + 0.05)^2.
Step 6: Calculate (1 + 0.05), which equals 1.05.
Step 7: Raise 1.05 to the power of 2: (1.05)^2 = 1.1025.
Step 8: Multiply the principal by the result: 1000 * 1.1025 = 1102.50.
Step 9: The final amount after 2 years is $1102.50.

Compound Interest – Understanding how interest is calculated on both the initial principal and the accumulated interest from previous periods.