Roger and Vanessa are planning to buy a house. The house will cost them $175,000, and they plan to make a $40,000 down payment and borrow the remaining $135,000. Roger and Vanessas monthly gross income is $3,700. Insurance is estimated to cost $800 per year, and taxes are estimated to be $1,000 per year. They plan to live in the house for 30 years. The house appraises right now for $182,000.

Currently, Roger and Vanessa are renting. Their monthly rent is $1,350. The rent typically increases at an annual rate of 4%.

Several purchase financing options are available. All would require a 1 point origination fee. Go ahead and compute the monthly payment for each loan option. Hint: on the ARM, you compute the initial PMT using the 4.3% and same as any 30-year loan.

Loan Term Type Rate Discount Points Payment APR

A 30 year fixed 5.5% 0 _______ ____

B 30 year fixed 5.4% 1 _______ ____

C 30 year 5/1 ARM 4.3%, then T-bill + 1% 0 _______ ____

D 15 year fixed 4.9% 0 _______ ____

E 15 year fixed 4.6% 1 _______ ____

Note: APR should be an additional blank column to the right

a. What is the present value of the rents paid over the next 30 years? To make the computation easier, assume that rent increases each month, and the nominal interest rate is 5%. Hint: this is a growing-payment annuity (due) problem.

b. Given the information above, would Roger and Vanessa qualify based on housing payment ratio for Loan A? Loan D?

c. What will be Roger and Vanessas L/V ratio? Will they need to buy mortgage insurance?

d. Suppose Roger and Vanessa buy the house. What is their initial equity value?

e. What is the APR for each of the five loans?

f. They are trying to decide between loan A and loan B. What is the break-even time on recovering the discount point?

g. They do not plan to pre-pay. Should they take loan A or loan B?

h. They do not plan to prepay. Should they take loan D or loan E?

i. How much total interest will they pay over the life of the loan in Loan A? Loan D?

j. When will be the first adjustment date on the ARM?

k. What is the spread, in basis points, between the highest and lowest rates on the loans?

l. Roger and Vanessa choose to finance the home purchase with Loan A. After their first monthly payment is made, the market value of their house is appraised at $185,000. What is the new value of equity in the house?

m. If Roger and Vanessa finance with Loan C, and at the first adjustment date, the T-bill rate is 4.5%, what will their monthly payment become if the balance remaining at that time is $120,000?

n. Roger expects to receive a $100,000 inheritance in 4 years that will be used to pre-pay the loan. Which loan is best?

o. What will be the balance in their escrow account after 6 months?

Now, assume that Roger and Vanessa have bought the home, using Loan A. Fifteen years have passed, and interest rate for a 15 year fixed is now 4.6%. Closing costs are $1,100, including loan origination fees. The current loan balance is $93,811. The home appraises at $190,000.

p. If they re-finance, what is their new payment? How many months until they recover their closing costs?

q. Should they re-finance?

r. Suppose they need more money for home improvements. How much money absolute maximum could they borrow with a Home equity loan?