A sum of $2000 is invested at a compound interest rate of 6% per annum. What wil

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Question: A sum of $2000 is invested at a compound interest rate of 6% per annum. What will be the amount after 5 years?

Options:

Correct Answer: $2676.28

Solution:

Amount = 2000(1 + 0.06)^5 = 2000(1.338225) = $2676.28.

A sum of $2000 is invested at a compound interest rate of 6% per annum. What will be the amount after 5 years?

A sum of $2000 is invested at a compound interest rate of 6% per annum. What will be the amount after 5 years?

Step 1: Identify the principal amount, which is $2000.
Step 2: Identify the annual interest rate, which is 6%. Convert this percentage to a decimal by dividing by 100, so 6% becomes 0.06.
Step 3: Identify the number of years the money is invested, which is 5 years.
Step 4: Use the compound interest formula: Amount = Principal * (1 + Rate)^Time.
Step 5: Substitute the values into the formula: Amount = 2000 * (1 + 0.06)^5.
Step 6: Calculate (1 + 0.06), which equals 1.06.
Step 7: Raise 1.06 to the power of 5: (1.06)^5 = 1.338225.
Step 8: Multiply the principal amount by the result: Amount = 2000 * 1.338225.
Step 9: Calculate the final amount: 2000 * 1.338225 = $2676.28.

Compound Interest – Understanding how compound interest works, including the formula for calculating the future value of an investment.
Exponential Growth – Recognizing that compound interest leads to exponential growth of the investment over time.
Mathematical Operations – Performing calculations involving powers and multiplication accurately.