If a sum of money is invested at a compound interest rate of 12% per annum, how

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Question: If a sum of money is invested at a compound interest rate of 12% per annum, how much will it grow in 2 years if the principal is $1500?

Options:

Correct Answer: $1680

Solution:

Total Amount = P(1 + r/100)^n = 1500(1 + 0.12)^2 = 1500(1.2544) = $1881.60.

If a sum of money is invested at a compound interest rate of 12% per annum, how much will it grow in 2 years if the principal is $1500?

If a sum of money is invested at a compound interest rate of 12% per annum, how much will it grow in 2 years if the principal is $1500?

Step 1: Identify the principal amount (P), which is $1500.
Step 2: Identify the annual interest rate (r), which is 12%.
Step 3: Convert the interest rate from percentage to decimal by dividing by 100. So, 12% becomes 0.12.
Step 4: Identify the number of years (n) the money is invested, which is 2 years.
Step 5: Use the compound interest formula: Total Amount = P(1 + r)^n.
Step 6: Substitute the values into the formula: Total Amount = 1500(1 + 0.12)^2.
Step 7: Calculate (1 + 0.12) = 1.12.
Step 8: Raise 1.12 to the power of 2: (1.12)^2 = 1.2544.
Step 9: Multiply the principal amount by the result: Total Amount = 1500 * 1.2544.
Step 10: Calculate the final amount: Total Amount = $1881.60.

Compound Interest – Understanding how compound interest works, including the formula for calculating the total amount after a certain number of years.
Mathematical Operations – Performing exponentiation and multiplication accurately to find the final amount.
Percentage Calculation – Converting the interest rate from a percentage to a decimal for calculations.