What is the future value of $1000 in an account for 9 years compounded bi monthly at 14%
1000(1+.14/6)^(6*9) = 3474.76
thanks!
To calculate the future value of $1000 in an account for 9 years compounded bi-monthly at 14%, we can use the formula for compound interest:
Future Value = Principal (1 + (Rate / n))^(n*t)
Where:
Principal = $1000
Rate = 14% (expressed as a decimal, 0.14)
n = number of compounding periods per year (bi-monthly compounding means 12 periods per year, so n = 12)
t = number of years (9 years in this case)
Plugging these values into the formula, we get:
Future Value = $1000 (1 + (0.14 / 12))^(12*9)
Now, let's calculate the future value step by step:
Step 1: Calculate the compound interest rate per period:
Rate per period = Rate / n
Rate per period = 0.14 / 12
Rate per period = 0.01166666667 (rounded to 11.67%)
Step 2: Calculate the number of total compounding periods:
Number of compounding periods = n * t
Number of compounding periods = 12 * 9
Number of compounding periods = 108
Step 3: Calculate the future value:
Future Value = Principal * (1 + Rate per period)^(Number of compounding periods)
Future Value = $1000 * (1 + 0.01166666667)^108
Using a calculator, we find that:
Future Value ≈ $3179.16
Therefore, the future value of $1000 in an account for 9 years compounded bi-monthly at a 14% interest rate is approximately $3179.16.