Over the past $40$ years, interest rates have varied widely. The rate for a $30-$year mortgage reached a high of $14\mathrm{.}75\%$ in July $1984,$ and it reached $3\mathrm{.}31\%$ in November $2012.$ A significant impact of lower interest rates on society is that they enable more people to afford the purchase of a home. In the following exercise, we consider the purchase of a home that sells for $$125,000.$ Assume that we can make a down payment of $$25,000,$ so we need to borrow $$100,000.$ We assume that our annual income is $$53,000$ and that we have no other debt.

If we can afford to pay a monthly amount of $$986\mathrm{.}67,$ determine how much we can borrow if the term is $30$ years and the interest rate is at the historic high of $14\mathrm{.}75\%.($Round your answer to the nearest dollar.$)$

$

$79282$

Incorrect: Your answer is incorrect.

Can we afford the home?

Yes

No

Correct: Your answer is correct.

If we can afford to pay a monthly amount of $$986\mathrm{.}67,$ determine how much we can borrow if the term is $30$ years and the interest rate is $3\mathrm{.}31\%.($Round your answer to the nearest dollar.$)$

$

Can we afford the home now?

Yes

No

Correct: Your answer is correct.

How much more can you afford to borrow when the $30-$year mortgage rate is at $3\mathrm{.}31\%$ compared to $14\mathrm{.}75\%?$

$

$121,605\mathrm{.}80$

Incorrect: Your answer is incorrect.