Bill and Kim Johnson are purchasing a house for $$252,000.$ Their Bank requires them to pay a $20\%$ down payment. The current mortgage rate is $10\%,$ and they are required to pay one point at the time of closing. Determine the total amount Bill and Kim will pay for their house, including principal, interest, down payment, and points $($do not include taxes and homeowners' insurance$)$ for the following lengths of their mortgage.

a$)10$ years

b$)20$ years

c$)30$ years