What is the annuity at the end of every 6months for 4 years which amounts to $2000 and money earns 6% compounded semi annually
To determine the annuity payment that amounts to $2000 at the end of 4 years with a 6% annual interest rate compounded semi-annually, we need to use the future value of an ordinary annuity formula:
FV = P * [(1 + r/n)^(nt) - 1] / (r/n)
Where:
FV = future value of the annuity (amounting to $2000 in this case)
P = annuity payment (what we are trying to find)
r = annual nominal interest rate (6% or 0.06 in decimal form)
n = number of compounding periods per year (2 for semi-annual)
t = number of years (4 in this case)
First, we need to find the semi-annual interest rate and the total number of compounding periods:
Semi-annual interest rate (r/n) = 0.06 / 2 = 0.03
Total number of compounding periods (nt) = 4 * 2 = 8
Now we can plug these values into the formula and solve for P:
$2000 = P * [(1 + 0.03)^8 - 1] / 0.03
$2000 = P * [(1.03)^8 - 1] / 0.03
$2000 = P * [1.26677 - 1] / 0.03
$2000 = P * [0.26677] / 0.03
$2000 = P * 8.89233
Now we can determine the annuity payment:
P = $2000 / 8.89233
P ≈ $224.89
So, the semi-annual annuity payment that would amount to $2000 at the end of 4 years, with a 6% annual interest rate compounded semi-annually, is approximately $224.89.