For Problems $6-11,$ assume you buy a home and borrow $$150,000$ at $4\mathrm{.}96\%$ for $30$ years. You pay a total of $$7,825$ for origination fee, points, and mortgage insurance. In addition, you pay other loan costs of $$1,685.$ You pay the first year's hazard insurance premium of $$475$ and are required to deposit $$380$ into an escrow account.

$6.$ What is the reportable APR?

$7.$ What is your real APR, assuming the loan is not paid off early?

$8.$ Without calculating a precise APR, decide if$,$ by prepaying the loan, your APR will be more or less than the APR found in Problem $7.$

$9.$ Assume you will pay off the loan at the end of $8$ years. What is your real APR, reflecting the early payoff?

$10.$ Assume, before you get this loan, you are offered another loan: $$150,000$ over $30$ years at $5\mathrm{.}10\%$ interest. You must pay loan costs totaling $$5,010($you save $$4,500$ in points for getting the higher interest rate loan$).$ Assuming you will pay off the loan at the end of $8$ years, what is your real APR on this loan, reflecting the early payoff?

$11.$ Refer to Problems $9$ and $10.$ Which loan has the lower APR?