Congratulations! You found the house of your dreams. The original price was $$350,000,$ but you

also have $$30,000$ to put in as a down payment and finance the rest with a $30-$year mortgage

with monthly payments and a $3\%$ annual interest rate.

a$)$ What is the monthly payment on this mortgage?

b$)$ After making the $100$th payment, you are informed of a re$-$financing opportunity that will

allow you take the balance you owe, then add $$3000,$ and then finance this a $15-$year

mortgage with an annual interest rate of $2\mathrm{.}5\%.$

i$)$ Find the balance that remains after the $100$th payment is made.

ii$)$ After the fee is added, how much is going to be financed with the new

mortgage?

iii$)$ What is the new mortgage payment?

iv$)$ Had you not refinanced, how much interest would you have paid on the rest of

the loan after the $100$th payment?

v$)$ How much interest do you pay on the new refinance?

vi$)$ Based on your answers in iv and v$,$