Assume a loan and property with the following characteristics: Property value: $300,000; Down payment: $50,000; Loan type: Hybrid 5/25 payment option ARM; Initial rate: 4% annual; Fully-indexed rate: 1-year LIBOR + 3.5%; Adjustment period: once per year (every 12 months); Rate cap: adjusted rate can be no higher than fully-indexed rate at origination plus 4%; Rate floor: adjusted rate can be no lower than fully-indexed rate at origination minus 4% Assume 1-year LIBOR at origination is 1% and that 1-year LIBOR on the first reset date is 2.5%. Assume the borrower chooses to make the fully-amortizing payment for the first five years. At the end of the fifth year, they ask the lender to recast the loan. Recasting involves the borrower making a large lump sum payment in exchange for the lender reducing the fully-amortizing monthly payment by subtracting the lump sum from the remaining unpaid principal balance. In other words, a loan recast reduces the borrower's fully-amortizing payment from the year following the loan recast to the year in which the loan matures. In this case, assume the borrower made a lump sum payment of $51,118.78 at the end of the fifth year (following their final monthly payment in that year) in order to recast the loan. Assume also that the lender requires no fees for recasting. (In reality, lenders may require small recasting fees). Compute the following: 

(a) What is the fully-amortizing monthly payment prior to the recast? 

(b) What is the unpaid principal balance at the end of the fifth year after making the fully- amortizing payments for the duration of the initial rate term but prior to the recast? 

(c) What is the unpaid principal balance at the end of the fifth year following the recast?

 (d) What is the fully-amortizing payment during the first year following the recast?