Jacey obtains a 30-year 6/2 ARM at 4% with a 2/6 cap structure in the amount of $224,500. What is the monthly payment during the initial period?

In this case we have an ARM fixed for 6 years and adjust after the initial first 6 years every 2 years after. The basic idea behind a ARM is that the interest changes periodically, but since our ARM is fixed for 6 years, our going to calculate the monthly payment during the initial period using the formula: [tex]m= \frac{P( \frac{r}{12}) }{1-(1+ \frac{r}{12})^{-12t} } [/tex]
where
[tex]m[/tex] is the monthly payment
[tex]P[/tex] is the amount
[tex]r[/tex] is the interest rate in decimal form 
[tex]t[/tex] is the number years

First we need to convert our interest rate of 4% to decimal form by dividing it by 100%:
[tex] \frac{4}{100} =0.04[/tex]
We also know from our question that [tex]P=224500[/tex] and [tex]t=30[/tex], so lets replace those values into our formula to find the monthly payment:
[tex]m= \frac{224500( \frac{0.04}{12}) }{1-(1+ \frac{0.04}{12})^{-(12)(30)} } [/tex]
[tex]m=1071.80[/tex]

We can conclude that the monthly payment during the initial period is $1071.58