A principal of $2000 is invested at a compound interest rate of 5% per annum. Wh

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Question: A principal of $2000 is invested at a compound interest rate of 5% per annum. What will be the total amount after 2 years?

Options:

Correct Answer: $2205.00

Solution:

Amount = P(1 + r)^n = 2000(1 + 0.05)^2 = 2000(1.1025) = $2205.00.

A principal of $2000 is invested at a compound interest rate of 5% per annum. What will be the total amount after 2 years?

A principal of $2000 is invested at a compound interest rate of 5% per annum. What will be the total amount after 2 years?

Step 1: Identify the principal amount (P), which is $2000.
Step 2: Identify the annual interest rate (r), which is 5%. Convert this to decimal form by dividing by 100, so r = 0.05.
Step 3: Identify the number of years (n) the money is invested, which is 2 years.
Step 4: Use the compound interest formula: Amount = P(1 + r)^n.
Step 5: Substitute the values into the formula: Amount = 2000(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 the principal by this result: Amount = 2000 * 1.1025.
Step 9: Calculate the final amount: 2000 * 1.1025 = $2205.00.

Compound Interest – Understanding how compound interest works, including the formula used to calculate the total amount after a certain period.
Exponents – Applying exponent rules in the context of compound interest calculations.
Financial Literacy – Basic knowledge of investment principles and how interest affects the growth of an investment over time.