$1.$ A home mortgage of $$200,000$ with a fixed APR of $4\%$ for $30$ years.For each of the following problems:

a$.$ Calculate the monthly payment

b$.$ Determine the total amount paid over the term of the loan

c$.$ Of the total amount paid, how much of the total is interest?

$1.$ A home mortgage of $$200,000$ with a fixed APR of $4\%$ for $30$ years

$2.$ You borrow $$10,000$ for a period of $5$ years at a fixed APR of $6\mathrm{.}5\%$

$3.$ You borrow $$14,000$ for a car loan of $5$ years at a fixed APR of $4\mathrm{.}1\%$

$4.$ You borrow $$150,000$ for a period of $15$ years at a fixed APR of $5\%$

$5.$ A student loan of $$100,000$ with a fixed APR of $5\mathrm{.}5\%$ for $20$ years.