1.A homeowner purchases a property for $1,000,000. She finances the purchase with an 80% LTV, 30-year fully amortizing graduated payment mortgage (GPM) carrying a 10% interest rate. A 20% rate of graduation will be applied to monthly payments beginning year 3 and the beginning of year 5, only (so, fixed for two two-year periods and then fixed for all years 5, 6, 7, ). She will sell the home in year 6. What is the APR for the loan if the Reg-Z fees are 3% plus $10,000?

2.Compute the duration and convexity of a 10-year Treasury bond, with coupon 3% and price 102-13. Note: 1. Treasuries are semiannual. 2. The price quote aaa-bb means aaa+b/32 dollars. 3. Treasuries are NC bonds.

3. You have had a 15yr FA FRM at 8% for 5 years. The original principal was 800,000. You are considering a cash-out refi into a 30-year mortgage at 6%. The old mortgage has a prepay penalty of 3% if payoff occurs before year 8. The new mortgage has fixed fees of 3,000 and variable fees of 4%, and a prepay penalty of 2%. The additional cash is for a $50,000 car, and can be borrowed at 8% over 5 years, with upfront fees of 3%.

Assume that all fees will be financed, and that under either scenario you will be moving 15 years from now. Ignore taxes, the option to wait to refinance, and assume no loan is prepaid, curtailed, nor ever defaults.

What is the NPV of refinancing if the opportunity cost of capital is 7%? [15] A constant payment (aka level payment) mortgage for $300,000 is to be made for 30 years at a contract rate of 6%. The loan is fully amortizing, all payments are monthly and are made according to schedule.

[2] What are the monthly payments?

[2] What will the loan balance be after 7 years?

[3] If the lender charges 2 points to close the loan, what is the APR of the loan if it is fully amortizing?

[3] The lender charges 2 points in upfront fees. If the borrower repays the loan after 7 years and owes a prepayment penalty of 2% of outstanding principal, what is the effective cost of the loan?

[5] Consider the same conditions as in D, but the lender will reduce the contract rate by 25bps if the borrower prepays an additional 1 point. Which product should the borrower choose, this loan or the one in D?

[15] A homeowner purchases a property for $1,000,000. She finances the purchase with an 80% LTV, 30-year fully amortizing graduated payment mortgage (GPM) carrying a 10% interest rate. A 20% rate of graduation will be applied to monthly payments beginning year 3 and the beginning of year 5, only (so, fixed for two two-year periods and then fixed for all years 5, 6, 7, ). She will sell the home in year 6. What is the APR for the loan if the Reg-Z fees are 3% plus $10,000?

[15] Compute the duration and convexity of a 10-year Treasury bond, with coupon 3% and price 102-13. Note: 1. Treasuries are semiannual. 2. The price quote aaa-bb means aaa+b/32 dollars. 3. Treasuries are NC bonds.

[15] You have had a 15yr FA FRM at 8% for 5 years. The original principal was 800,000. You are considering a cash-out refi into a 30-year mortgage at 6%. The old mortgage has a prepay penalty of 3% if payoff occurs before year 8. The new mortgage has fixed fees of 3,000 and variable fees of 4%, and a prepay penalty of 2%. The additional cash is for a $50,000 car, and can be borrowed at 8% over 5 years, with upfront fees of 3%.

Assume that all fees will be financed, and that under either scenario you will be moving 15 years from now. Ignore taxes, the option to wait to refinance, and assume no loan is prepaid, curtailed, nor ever defaults.

What is the NPV of refinancing if the opportunity cost of capital is 7%? [15] A constant payment (aka level payment) mortgage for $300,000 is to be made for 30 years at a contract rate of 6%. The loan is fully amortizing, all payments are monthly and are made according to schedule.

[2] What are the monthly payments?

[2] What will the loan balance be after 7 years?

[3] If the lender charges 2 points to close the loan, what is the APR of the loan if it is fully amortizing?

[3] The lender charges 2 points in upfront fees. If the borrower repays the loan after 7 years and owes a prepayment penalty of 2% of outstanding principal, what is the effective cost of the loan?

[5] Consider the same conditions as in D, but the lender will reduce the contract rate by 25bps if the borrower prepays an additional 1 point. Which product should the borrower choose, this loan or the one in D?

[15] A homeowner purchases a property for $1,000,000. She finances the purchase with an 80% LTV, 30-year fully amortizing graduated payment mortgage (GPM) carrying a 10% interest rate. A 20% rate of graduation will be applied to monthly payments beginning year 3 and the beginning of year 5, only (so, fixed for two two-year periods and then fixed for all years 5, 6, 7, ). She will sell the home in year 6. What is the APR for the loan if the Reg-Z fees are 3% plus $10,000?

[15] Compute the duration and convexity of a 10-year Treasury bond, with coupon 3% and price 102-13. Note: 1. Treasuries are semiannual. 2. The price quote aaa-bb means aaa+b/32 dollars. 3. Treasuries are NC bonds.

[15] You have had a 15yr FA FRM at 8% for 5 years. The original principal was 800,000. You are considering a cash-out refi into a 30-year mortgage at 6%. The old mortgage has a prepay penalty of 3% if payoff occurs before year 8. The new mortgage has fixed fees of 3,000 and variable fees of 4%, and a prepay penalty of 2%. The additional cash is for a $50,000 car, and can be borrowed at 8% over 5 years, with upfront fees of 3%.

Assume that all fees will be financed, and that under either scenario you will be moving 15 years from now. Ignore taxes, the option to wait to refinance, and assume no loan is prepaid, curtailed, nor ever defaults.

What is the NPV of refinancing if the opportunity cost of capita