Suppose that you take out a $20$ year mortgage of $$200,000$ from PNC$.$ Assume that the payments are made annually. Which of the following payment schedule will allow PNC to earn a $5\%$ annualized rate of return from the loan assuming that all the payments will be made?

a$)$ $$8000$ payment every year for the next twenty years plus a payment of $$200,000$ in year $20.$

b$)$ $$16,048\mathrm{.}5$ payment every year for the next twenty years.

Please show the calculations behind your choice. Show both why your choice is correct and why the other one is not correct.