Help me understand this question
An investment account earns 4% per year compounded annually. If the initial investment was $4,000.00, how much is in the account after 3 years? Round your answer to the nearest dollar.
This question is asking you to calculate the future value of an investment account after 3 years, given that the account earns 4% interest compounded annually.
To calculate the future value, you can use the formula for compound interest:
Future Value = Initial Investment * (1 + (Interest Rate/100))^Number of Years
Plugging in the values given in the question:
Future Value = $4,000.00 * (1 + (4/100))^3
Future Value = $4,000.00 * (1 + 0.04)^3
Future Value = $4,000.00 * (1.04)^3
Future Value = $4,000.00 * 1.124864
Future Value ≈ $4,499.46
So, after 3 years, there would be approximately $4,499.46 in the account. Rounded to the nearest dollar, this would be $4,499.
why is there a one
I apologize for the confusion. The "1" in the formula represents the initial amount of the investment, which is multiplied by the growth factor to calculate the future value.
So, in the context of compound interest calculations, the "1" represents the initial investment amount that is used as the starting point for calculating the growth over time. It essentially ensures that the initial investment amount is taken into account when determining the final value after the specified number of years.
If you have any further questions, please let me know.
why is there ^3
The "^3" in the formula represents raising the growth factor to the power of 3 because the investment is compounded annually for 3 years.
In the formula for compound interest, raising the growth factor to the power of the number of years indicates how many times the interest is compounded over the given period. In this case, the interest is compounded annually, so the growth factor needs to be raised to the power of 3 for 3 years.
Essentially, raising the growth factor to the power of the number of years accounts for the compounding effect of interest over time and allows you to calculate the future value of the investment after a specific number of compounding periods.
I hope this helps clarify the use of "^3" in the formula for calculating compound interest. Let me know if you have any more questions.