You are considering buying your first home in Pahrump. Your dream home is available

with a list price of $$450,000.$ Assuming you agree to the list price as the purchase price and put $10\%$ down, what is your monthly mortgage payment if:a$.$ You take out a $30-$year mortgage with a $4\mathrm{.}25\%$ interest rate, compounded monthly?b$.$ You take out a $15-$year mortgage with a $3\mathrm{.}33\%$ interest rate, compounded monthly?