Question

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?

Answer 1

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: $m= \frac{P( \frac{r}{12}) }{1-(1+ \frac{r}{12})^{-12t} }$
where
$m$ is the monthly payment
$P$ is the amount
$r$ is the interest rate in decimal form 
$t$ is the number years

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

We can conclude that the monthly payment during the initial period is $1071.58<span />