What is the future value of $4000 in a bank for 9 years at 12% compounded bi monthly rounded to the nearest cent.
To calculate the future value of $4000 over 9 years at an annual interest rate of 12% compounded bi-monthly, we can use the compound interest formula:
Future Value = Principal * (1 + (interest rate / number of periods))^(number of periods * number of years)
In this case:
Principal = $4000
Interest rate = 12% (converted to its decimal form of 0.12)
Number of periods per year = 12 (since interest is compounded bi-monthly)
Number of years = 9
Let's now calculate the future value step-by-step:
Step 1: Convert the bi-monthly interest rate to a monthly interest rate.
Bi-monthly interest rate = (Annual interest rate / Number of periods per year) = 0.12 / 12 = 0.01
Step 2: Calculate the number of periods.
Number of periods = Number of periods per year * Number of years = 12 * 9 = 108
Step 3: Plug the values into the formula and calculate the future value.
Future Value = $4000 * (1 + 0.01)^(108) = $4000 * (1.01)^(108) ≈ $8030.75
Therefore, the future value of $4000 in a bank for 9 years at 12% compounded bi-monthly, rounded to the nearest cent, is approximately $8030.75.