A popular mortgage in some regions was the option ARM. As option ARM

comes with several payment options, including a minimum payment option based on a short$-$term teaser rate that has a maximum annual payment increase feature like a graduated payment mortgage. Consider a $$150,000,30$ year option ARM with index rate $=1$ year LIBOR, margin $=3\%,$ and a one month teaser rate of $1\mathrm{.}25\%.$ Suppose that $1$ year LIBOR is $2\%$ for the first year and $4\%$ for the second year of the loan. The teaser rate lasts only one month, after which the rate becomes the fully indexed rate. Although the teaser rate lasts only one month, the first year$$s payment is based on the teaser rate. $($It is computed as you would the first year$$s payment on a $1/1$ ARM using the teaser rate as the rate for entire year.$)$

a$.$ Compute the first year$$s minimum monthly payment. Compute

amortization over the first $12$ months based on the minimum payment

recognizing that the rate beginning in month $2$ will no longer be $1\mathrm{.}25\%,$

but the payment is fixed for entire first year. What is the principle balance

at the end of year $1?$

b$.$ Assume that the minimum payment increases by $7\mathrm{.}5\%$ per year. What will

the loan rate be in year $2?$ What will amortization be in month $13$ under

the minimum payment option?