# 5 Use the following rate tree . Short rate can increase or decrease in 6 months by equal probability . Use semi- annual compounding . Time O Time 0. 5 10% 12% or 8% Now , consider a 1 year mortgage ( semi - annually paid ) with a semi - annual mortgage rate of 10% and an initial principal balance of $70 , 000 . The mortgage is divided into three sequential pay tranches . Tranche A receives the first $3 , 000 of principal , tranche* B receives the next $3 , 000 of principal , and tranche C receives the remaining $4 , 000 of principal . Fill in the amortization schedule of the whole mortgage below . Date Beginning Scheduled Scheduled Ending ( Year ) Principal Semi - annual Semi - annual Principal Principal Balance Payment Interest Repayment* Balance 0. 5 1. 0