**1.**A price level adjusted mortgage (PLAM) is made with the following terms:

Amount = $95,000

Initial interest rate = 4 percent

Term = 30 years

Points = 6 percent

Payments to be reset at the beginning of each year

Assuming inflation is expected to increase at the rate of 6 percent per year for the next five years:

a.Compute the payments at the beginning of each year (BOY).

b.What is the loan balance at the end of the fifth year?

c.What is the yield to the lender on such a mortgage?

**1b.**In the previous chapter, significant problems regarding the ability of borrowers to meet mortgage payments and the evolution of fixed interest rate mortgages with various payment patterns were discussed. Why didn’t this evolution address problems faced by lenders? What have lenders done in recent years to overcome these problems?

** ****2a. **A basic ARM is made for $200,000 at an initial interest rate of 6 percent for 30 years with an annual reset date. The borrower believes that the interest rate at the beginning of year (BOY) 2 will increase to 7 percent.

Assuming that a fully amortizing loan is made, what will monthly payments be during year 1?

b.Based on (a) what will the loan balance be at the end of year (EOY) 1?

c.Given that the interest rate is expected to be 7 percent at the beginning of year 2, what will monthly payments be during year 2?

d.What will be the loan balance at the EOY 2?

e.What would be the monthly payments in year 1 if they are to be interest only?

f.Assuming terms in (e), what would monthly interest only payments be in year 2?

**2b.**How do inflationary expectations influence interest rates on mortgage loans?

**3a. **A 3/1 ARM is made for $150,000 at 7 percent with a 30-year maturity.

a.Assuming that fixed payments are to be made monthly for three years and that the loan is fully amortizing, what will be the monthly payments? What will be the loan balance after three years?

b.What would new payments be beginning in year 4 if the interest rate fell to 6 percent and the loan continued to be fully amortizing?

c.In (a) what would monthly payments be during year 1 if they were interest only? What would payments be beginning in year 4 if interest rates fell to 6 percent and the loan became fully amortizing?

**3b.**How does the price level adjusted mortgage (PLAM) address the problem of uncertainty in inflationary expectations? What are some of the practical limitations in implementing a PLAM program?

**4a.** An ARM for $100,000 is made at a time when the expected start rate is 5 percent. The loan will be made with a teaser rate of 2 percent for the first year, after which the rate will be reset. The loan is fully amortizing, has a maturity of 25 years, and payments will be made monthly.

a.What will be the payments during the first year?

b.Assuming that the reset rate is 6 percent at the beginning of year (BOY) 2, what will payments be?

c.By what percentage will monthly payments increase?

d.What if the reset date is three years after loan origination and the reset rate is 6 percent, what will loan payments be beginning in year 4 through year 25?

**4b**. Why do adjustable rate mortgages (ARMs) seem to be a more suitable alternative for mortgage lending than PLAMs?

**5a.** An interest only ARM is made for $200,000 for 30 years. The start rate is 5 percent and the borrower will (1) make monthly interest only payments for 3 years. Payments thereafter must be sufficient to fully amortize the loan at maturity.

a. If the borrower makes interest only payments for 3 years, what will payments be?

b. Assume that at the end of year 3, the reset rate is 6 percent. The borrower must now make payments so as to fully amortize the loan. What will payments be?

**5b.** List each of the main terms likely to be negotiated in an ARM. What does pricing an ARM using these terms mean?

**6a.**A borrower has been analyzing different adjustable rate mortgage (ARM) alternatives for the purchase of a property. The borrower anticipates owning the property for five years. The lender first offers a $150,000, 30-year fully amortizing ARM with the following terms:

Initial Interest rate=6 percent

Index=1 year Treasuries

Payments reset each year

Margin=2 percent

Interest rate cap=None

Payment cap=None

Negative amortization=Not allowed

Discount points=2 percent

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

**6b.** What is the difference between interest rate risk and default risk? How do combinations of terms in ARMs affect the allocation of risk between borrowers and lenders?

**7a.**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, loan balances, and yield for the ARM for the five-year period.

** **

**7b.** Which of the following two ARMs is likely to be priced higher, that is, offered with a higher initial interest rate?ARM A has a margin of 3 percent and is tied to a three-year index with payments adjustable every two years; payments cannot increase by more than 10 percent from the preceding period; the term is 30 years and no assumption or points will be allowed. ARM B has a margin of 3 percent and is tied to a one-year index with payments to be adjusted each year; payments cannot increase by more than 10 percent from the preceding period; the term is 30 years and no assumption or points are allowed.

**8a.** Assume that a lender offers a 30-year, $150,000 adjustable rate mortgage (ARM) with the following terms: ** **

Initial Interest rate=7.5 percent

Index=1 year Treasuries

Payments reset each year

Margin=2 percent

Interest rate cap=1 percent annually;3 percent lifetime

Discount points=2 percent

Fully amortizing; however, negative amortization allowed if interest rate caps 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, loan balances, and yield for the ARM for the five-year period.

**8b.** What are forward rates of interest? How are they determined? What do they have to do with indexes used to adjust ARM payments?

**9a. **MakeNu Mortgage Company is offering a new mortgage instrument called the Stable Mortgage. This mortgage is composed of both a fixed rate and an adjustable rate component. Mrs. Maria Perez is interested in financing a property, which costs $100,000, and is to be financed by Stable Home Mortgages (SHM) on the following terms:

a.The SHM requires a 5 percent down payment, costs the borrower 2 discount points, and allows 75 percent of the mortgage to be fixed and 25 percent to be adjustable. The fixed portion of the loan is for 30 years at an annual interest rate of 10.5 percent. Having neither an interest rate nor payment cap, the adjustable portion is also for 30 years with the following terms:

** **

Initial Interest rate=9 percent

Index=1 year Treasuries

Payments reset each year

Margin=2 percent

Interest rate cap=None

Payment cap =None

The project one-year U.S Treasury bill index,to which the ARM is tied,is as follows:

(BOY) 2=10 percent;(BOY) 3=11 percent;(BOY) 4=8 percent;(BOY) 5=12 percent

Calculate Mrs. Perez’s total monthly payments and end-of-year loan balances for the first five years. Calculate the lender’s yield, assuming Mrs. Perez repays the loan after five years.

b.Repeat part (a) under the assumption that the initial interest rate is 9.5 percent and there is an annual interest rate cap of 1 percent.

** **

**9b.** Distinguish between the initial rate of interest and expected yield on an ARM. What is the general relationship between the two? How do they generally reflect ARM terms?

**10a. **A floating rate mortgage loan is made for $100,000 for a 30-year period at an initial rate of 12 percent interest. However, the borrower and lender have negotiated a monthly payment of $800.

a.What will be the loan balance at the end of year 1?

b.What if the interest rate increases to 13 percent at the end of year 1? How much interest will be accrued as negative amortization in year 1 if the payment remains at $800? Year 5?

**10b.** If an ARM is priced with an initial interest rate of 8 percent and a margin of 2 percent (when the ARM index is also 8 percent at origination) and a fixed rate mortgage (FRM) with constant payment is available at 11 percent, what does this imply about inflation and the forward rates in the yield curve at the time of origination? What is implied if a FRM were available at 10 percent? 12 percent?

**11.**Excel. Refer to the “Ch5 ARM No Caps” tab in the Excel Workbook provided on the Web site. Suppose the index goes to 18 percent in year 5. What is the effective cost of the unrestricted ARM?

**12.**Excel. Refer to the “Ch5 ARM Int Cap” tab in the Excel Workbook provided on the Web site. Suppose the index goes to 18 percent in year 5. What is the effective cost of this ARM? What cap affected the rate in year 5?

**13.**Excel. Refer to the “Ch5 ARM Pmt Cap” tab in the Excel Workbook provided on the Web site. Suppose the index goes to 18 percent in year 5. What is the effective cost of the ARM? Does the payment cap keep the effective cost from rising?

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