Consider the following pair of options for a $$100,000$ mortgage.

Option $1$: $15-$year fixed rate at $5\%.$

Option $2$: $30-$year fixed rate at $6\mathrm{.}5\%.$

a$.$ What is the monthly payment for Option $1?$

b$.$ What is the total payment over the lifetime of the loan for Option $1?$

c$.$ What is the monthly payment for Option $2?$

d$.$ What is the total payment over the lifetime of the loan for Option $2?$

e$.$ Based on the amounts you calculated for #a$-$d$,$ which Option would you choose? Explain why you selected that Option.