1. A bank makes a 30 year Fully Amortizing FRM for $100,000 at an annual interest rate of 7% compounded monthly, with monthly payments. What is the difference (in dollars) between the balance and the market value of the loan after 17 monthly payments if the interest rate rises to 9%?

(Give the absolute value of the difference, so the answer should be a positive number.)

2. A bank makes a 30 year Fully Amortizing FRM for $100,000 at an annual interest rate of 7% compounded monthly, with monthly payments. Suppose inflation is 2% per year, compounded monthly. What is the real value of the 120^th payment?

3. Assume the initial rate on a 1/1 ARM is 4.50%. The loan has a margin of +200 basis points above Libor subject to a 5/2/5 rate cap structure.

What is the maximum rate the loan can reset to on its 1^st reset date?

4. Assume the initial rate on a 1/1 ARM is 4.50%. The loan has a margin of +200 basis points above Libor subject to a 5/2/5 rate cap structure.

What would the minimum rate on the index need to be if the cap were hit on the first reset?

5. Assume the initial rate on a 1/1 ARM is 4.50%. The loan has a margin of +200 basis points above Libor subject to a 5/2/5 rate cap structure.

If the Libor was at 1.00% at the time of the 1^st reset and then subsequently reached 3.25% by the time of the 2^nd reset what rate would the mortgage reset to for year 3?

(Hint: the rate at the first reset applies to payments in year 2, the rate at the second reset applies to payments in year 3.)

6. Tim wants to buy an apartment that costs $600,000 with an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 3.25%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. Tim anticipates the index to be 3.50% at the time of the 1^st reset.

What is Tims monthly mortgage payment going to be during the 1^st 3 years?

7. Tim wants to buy an apartment that costs $600,000 with an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 3.25%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. Tim anticipates the index to be 3.50% at the time of the 1^st reset.

If the index resets to 3.50% as Tim forecasts, what will his new mortgage payment be in year 4?

8. Tim wants to buy an apartment that costs $600,000 with an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 3.25%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. The index was 1% at the time of origination. Tim also had to pay 1 point for this loan.

Compute the true APR (annualized IRR) for this loan.

9. Tim wants to buy an apartment that costs $600,000 with an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 3.25%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. The index was 1% at the time of origination. Tim also had to pay 1 point for this loan.

Suppose the index rate will remain 1% for the life of the loan. Compute the annualized IRR for this loan assuming Tim will prepay in 5 years.

10. Bob got a 30 year Fully Amortizing FRM for $100,000 at 5%, except with non-constant payments. For the first 2 years Bob will pay $400 per month. The loan will fully amortize after 2 years. What will be the balance on this mortgage after 2 years?

(hint: see slides 50-51 in the ARM lecture)

11. Tom got a 30 year fully amortizing FRM for $400,000 at 6%, with constant monthly payments. After 3 years of payments rates fall and he can get a 27 year FRM at 5%, but he must pay 2 points and $1500 in closing costs to get the new loan. Think of the refinancing decision as an investment for Tom, he pays a fee now but saves money in the future in the form of lower payments. What is the annualized IRR of refinancing for Tom assuming he stays until maturity?

12. Tom got a 30 year fully amortizing FRM for $400,000 at 6%, with constant monthly payments. After 3 years of payments rates fall and he can get a 27 year FRM at 5%, but he must pay 2 points and $1500 in closing costs to get the new loan. Think of the refinancing decision as an investment for Tom, he pays a fee now but saves money in the future in the form of lower payments. What is the annualized IRR of refinancing for Tom assuming he prepays the new loan in 5 years?

(Clarification: Tom will prepay the new loan 5 years after the house is purchased)