You are considering making a mortgage loan with the following characteristics:

Loan amount: $$100,000$

monthly interest rate: $\mathrm{.}004$

Amortization: $300$ months

Term $60$ months

You believe that there is a $5\%$ probability that the borrower will default at month $30.$ In that event, you will receive $29$ regular payments and receive a terminal payoff in default of $$50,000$ in month $30.$

With the remaining $95\%$ probability, you expect to receive all $60$ regular payments and the outstanding balance due at month $60.$ If you are risk neutral and discount at a rate of $\mathrm{.}003$ per month, what would be the expected NPV of this loan to you $($recognizing the $$100,000$ loan amount as an immediate cost$)?$