what is the future value of $4000 at 6% compounded semiannually for nine years rounded to the nearest cent?
what is
4000(1.03)^18 ?
That is what I came up with, so when I do my calculation as followed 4000 x 1.03 i get 4120. I understand the ^18 is coming the 2x9, but somehow I'm confused on the next step after my first calculation step.
To calculate the future value of an investment, we will use the formula for compound interest:
Future Value = Principal * (1 + Interest Rate / Number of Compounding Periods)^(Number of Compounding Periods * Number of Years)
In this case, the principal is $4000, the interest rate is 6%, and the investment compounds semiannually for nine years.
Step 1: Convert the interest rate to decimal form:
Interest Rate = 6% = 0.06
Step 2: Calculate the number of compounding periods:
Since the investment compounds semiannually, there are two compounding periods per year:
Number of Compounding Periods = 2
Step 3: Calculate the future value:
Future Value = $4000 * (1 + 0.06 / 2)^(2 * 9)
Now, let's solve the equation:
Future Value = $4000 * (1 + 0.03)^(18)
Future Value = $4000 * (1.03)^(18)
Future Value = $4000 * 1.66268260939
Using a calculator or a spreadsheet application, we can find the product:
Future Value ≈ $6,650.73
Thus, the future value of $4000 at a 6% interest rate compounded semiannually for nine years is approximately $6,650.73.