You have just purchased a home and taken out a $$470,000$ mortgage. The mortgage has a $30-$year term with monthly payments and an APR of $5\mathrm{.}04\%.$

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 $20$th year $($i$.$e$.,$ between $19$ and $20$ years from now$)?$

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

The principal payment will be $$\_.($Round to the nearest cent.$)$

The interest payment will be $$,($Round to the nearest cent.$)$

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

The principal payment is $$.($Round to the nearest cent.$)$

The interest payment is $$,($Round to the nearest cent.$)$