If $1200 is invested at a rate of 5% per annum compounded annually, what will be

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Question: If $1200 is invested at a rate of 5% per annum compounded annually, what will be the total amount after 4 years?

Options:

Correct Answer: $1464

Solution:

Amount = 1200(1 + 0.05)^4 = 1200(1.21550625) = $1458.61.

If $1200 is invested at a rate of 5% per annum compounded annually, what will be the total amount after 4 years?

If $1200 is invested at a rate of 5% per annum compounded annually, what will be the total amount after 4 years?

Step 1: Identify the principal amount (the initial investment), which is $1200.
Step 2: Identify the annual interest rate, which is 5%. Convert this percentage to a decimal by dividing by 100: 5% = 0.05.
Step 3: Identify the number of years the money is invested, which is 4 years.
Step 4: Use the formula for compound interest: Amount = Principal × (1 + Rate)^Time.
Step 5: Substitute the values into the formula: Amount = 1200 × (1 + 0.05)^4.
Step 6: Calculate (1 + 0.05), which equals 1.05.
Step 7: Raise 1.05 to the power of 4: (1.05)^4 = 1.21550625.
Step 8: Multiply the principal amount by the result from Step 7: Amount = 1200 × 1.21550625.
Step 9: Calculate the final amount: 1200 × 1.21550625 = $1458.61.

Compound Interest – Understanding how to calculate the total amount of an investment over time with a fixed interest rate compounded annually.
Exponential Growth – Recognizing that the amount grows exponentially due to compounding, rather than linearly.