$1.$ You need to borrow $$3,500,000$ to finance the purchase of an apartment building. You have two loan alternatives to choose from. The first alternative has $7\mathrm{.}1$ percent interest for $30$ years, with $3$ points to be included in closing costs. The second alternative has $7\mathrm{.}5$ percent interest for $30$ years, with $1$ point to be included in the closing costs.

a$.$ If the loan is repaid after $10$ years, which alternative would be the better choice?

b$.$ If the loan is repaid after five years, which alternative is the better choice?