You have just purchased a home and taken out a

$580,000

mortgage. The mortgage has a

30-year

term with monthly payments and an APR (with semi-annual compounding) of

7.5%.

a. How much will you pay in interest, and how much will you pay in principal, during the first year?

b. How much will you pay in interest, and how much will you pay in principal, during the 20th year (i.e., between 19 and 20 years from now)?