Dan got a $10$ year Fixed Rate Mortgage for $$100,000.$

The loan has constant annual payments and an annual interest rate of $5\%.$

The closing cost for the loan is $$2,000($paid at the time of origination, t$=0).$

Suppose Dan prepays the loan in year $4.$

Write the NPV of Dan$$s Mortgage $($from Dan$$s perspective$)$ for an annual discount rate $"$k$"$ in each of the following cases.

Note: the answer must take the form

NPV$($k$)=$CF$\_0+($CF$\_1)/(1+$k$)^1+($CF$\_2)/(1+$k$)^2+($CF$\_3)/(1+$k$)^3+($CF$\_4)/(1+$k$)^4$

Note: only include one cash$-$flow for each time period

A$.$ Fully Amortizing

B$.$ Partially Amortizing where the final balance is B$\_10=$$$50,000$

C$.$ Interest Only

Part D: Compute the IRR for each loan above.