Problem 1 (Textbook: chapter 5, problem 7). An ARM is made for $150,000 for 30 years with the following terms: Initial interest rate = 7 percent Index = 1-year Treasuries Payments reset each year Margin = 2 percent Interest rate cap = None Payment cap = 5 percent increase in any year Discount points = 2 percent Fully amortizing; however, negative amortization allowed if payment cap reached Based on estimated forward rates, the index to which the ARM is tied is forecasted as follows: Beginning of year (BOY) 2 = 7 percent; (BOY) 3 = 8.5 percent; (BOY) 4 = 9.5 percent; (BOY) 5 = 11 percent. Compute the payments and loan balances for the ARM for the five-year period. Not reguired for the HW or Exam, but if you have time and want to practice, calculate the yield for the five- year period. Solution 5-7 Compute the payments, loan balances, and yield for an ARM that has a maximum 5% annual payment cap and does allow negative amortization. Principal : $150,000 Term = 30 years Points = 2.00% Initial Rate : 7.0% (1) (2) (3) (4) (5) BOY Uncapped Payment Pament EOY Rate Balance Balance Uncapped Capped 1 $150,000 7.00% $997.95 $997.95 $148,476 2 $148,476 9.00% $1,202.89 $1,047.85 $149,298 3 $149,298 10.50% $1,380.27 $1, 100.24 $151,894 4 $151,894 11.50% $1,525.03 $1,155.26 $155,695 5 $155,695 13.00% $1,747.28 $1,213.02 $161,731 6 $161,731 Note: EOY Balance is calculated by using: FV(n,i,pv,pmt) PV = Loan amount 11 : 12 months i : Uncapped rate PMT : Capped payment FV : Calculator: IRR(CF1, CF2, ....CFn) CF, nj $147,000 997.95 n = 12 1047.85 n : 12 1100.24 n : 12 1155.26 n = 12 1213.02 11 = 11 1213.02 + 161,731 n : 1 Solve for the IRR: : 0.8706076 X 12 : 10.45% (annual rate. compounded monthly]