## Sharon plans to borrow from a bank to finance her investment in a real estate project. She considers an ARM loan with three-year loan term, $100,000 loan amount. The loan has the following terms:

Sharon plans to borrow from a bank to finance her investment in a real estate project. She considers an ARM loan with three-year loan term, $100,000 loan amount. The loan has the following terms: 1) initialinterest rate =8.5%; 2)margin = 3%; 3) loan amortization period = 15 years; 4) frequency of adjustment = 1 year(monthly compounding); 5) interest rate cap = none; 6) payment cap = none; and 7)discount points = 3%; 8) no negative amortization is allowed. The index rates (i.e., based on 3 year treasure rate) for next two years (i.e., the 2nd and 3rd year) are expected to be 11% and 8%, respectively.

(a) If the loan will be repaid after 3 years, what would be the monthly payment and the ending loan balance for each of the three years? [2pts] IS THIS RIGHT

100,000×3%= PV 97,0000 I 8.5% N 180

Year 1 Year 2 Year 3

PV 97,000 PV 93,654.28 PV 90,789.82

I 8.5% I 11.5% I 11.5%

N 15×12=180 N14x12=168 N 14×12=168

PMT $955.30 / 93,654.28 PMT $1,123.90 /$90,789.82 PMT $1,123.90 /$87,578.02

(b) What isthe effective mortgage yield for borrowing this mortgage? [5pts]

(c) Now suppose that there is an annual interest rate cap of 2% specified in the loan contract. What isthe effective mortgage yield for borrowing this mortgage, assuming that no negative amortization is allowed? [5pts]

(d) Now suppose, instead of the annual interest rate cap of 2%, the bank prefers a 3% annual payment cap. Assume that negative amortization is allowed, what is the effective mortgage yield for borrowing this mortgage? [3 pt

1. Luistook a mortgage loan 5 years ago for $120,000 at 7% interest for 15 years, to be paid in monthly payments. Now, a lender is offering him a new mortgage loan at 5% for 10 years. The new loan amount is $92,895, the outstanding loan balance of the existing loan. Suppose that a prepayment penalty of 3 % must be paid if Luis refinances the existing loan. Moreover, the lender who is making the new loan requires an origination fee of $3,000. Luis plans to hold the property for 10 years. Note: in this case, Luis has to pay the refinancing fees (i.e., the origination fee and the prepayment penalty) out of his pocket.

(c) Now suppose thatLuis’s current income is low. The new lender allows him to pay a monthly payment of $200 for the new loan (i.e., the actual monthly payment to the lender is only $200, while the loan interest rate is 5%). In this situation, negative amortization occurs. What will be the accrued interest or the amount of increased loan balancefor the loan three years later from now? [3pts]

(d) Assume that Luis has to borrow two loans in order to refinance. That is, he has to borrow a new mortgage ($70,000) at 5% for 10 years (i.e., the loan maturity and the amortization period are the same, 10 years) and another mortgage ($22,895) at 9% for 5 years (the loan maturity and the amortization period are the same, 5 years). In this case, with the same