Let \(V_{k s}\) be the value of an adjustable-rate loan initiated at period \(k\) and state \(s\) with initial principal of 100 . The loan is to be fully paid at period \(n\). The interest rate charged each period is the short rate of that period plus a premium \(p\). The loan payment for a period is the amount that would be required to amortize the loan at the charged interest rate equally over the remaining periods. Write an explicit backward recursion formula for \(V_{k s}\) as a function of \(k\) and \(s\).