Option $3$ Adjustable Rate, $15$ years

Loan term: $15$ years, monthly payments

Annual interest rate: $5/1$ ARM, initial rate $5\mathrm{.}50\%,2\%$ annual cap, $8\%$ lifetime cap

Up front financing costs: $$6,000$

Discount points: $3$ points

Principle: $300,000$

$2.$ Based on your expected holding period, your friend encourages you to consider an adjustable rate mortgage option, Mortgage C$.$ Since you expect interest rates to fall over this period, assume the ARM will adjust to $5\mathrm{.}00\%$ for year $6$ and $4\mathrm{.}75\%$ for year $7.$ Set up the $7-$year loan amortization schedule for the ARM option.

a$.$ How much in total payments will you make under the ARM option?

b$.$ How much in total interest will you pay under the ARM option?

c$.$ What will be the outstanding loan balance at the end of year $7$ for the ARM option?

d$.$ Calculate the effective borrowing cost for the ARM option.

e$.$ Given all three options $(1,2,$ or $3),$ which loan would you choose? Did your decision change from the original fixed rate options in question $1?$ Why or why not?