The Wilson$$s are considering the purchase of a new home. They have enough money saved for

a $$100,000$ down payment, but will need to take out a mortgage for $$500,000.$ The bank has

offered a $5$ year rate of $6\mathrm{.}3\%,$ compounded monthly

a$)$ What is the monthly mortgage payment if the Wilson$$s spread the loan over $25$ years?

b$)$ Of the first mortgage payment, how much is to pay interest and how much goes toward

paying down the

c$)$ principal?

d$)$ How much is owing on the mortgage after $5$ years?

e$)$ Over the $25$ years, how much interest is paid?

f$)$ Suppose they spread the payments over $20$ years instead. What is the monthly payment?

g$)$ How much is still owing after $5$ years?

h$)$ What is the total interest paid over the $20$ years?