Chapter 9: ANSWERS TO "DO YOU UNDERSTAND" TEXT QUESTIONS
DO YOU UNDERSTAND?
1. If you had a 9 percent, $100,000, 15-year mortgage, and you paid it as scheduled, how much interest would you pay in the first month of the sixth year on that mortgage? How much principal would you pay?
Solution: $600.09 in interest would be due on the 15-year mortgage, so the balance of the $1,015 total monthly payment, or $414.91, would be used to pay down the principal due.
2. What would your principal and interest payments be if the mortgage were a 30-year mortgage at 9 percent? (Hint: See Exhibit 9.1 and carry the calculations forward in a spreadsheet.)
Solution: Interest on the 30-year mortgage would be $718.89 and the remainder of the payment, or $86.61, would be repayment of principal. These can be calculated by first calculating 0.75 percent interest (9 percent interest on an annual basis is 0.75 percent per month) on the balance due after the fifth year’s 12th month, and then subtracting that amount from the monthly payment.
3. If you had a mortgage with an initial rate of 5 percent that adjusted its rate once a year to equal the one-year Treasury bill rate plus 2.75 percent, with a cap on rate increases of 2 percent per year and 5 percent rate increase cap over the life of the mortgage, what rate would you pay in the second year of the mortgage if the one-year Treasury bill rate was 4.5 percent when the new rate was calculated?
Solution: 7 percent. Due to the 2 percent cap on annual rate increases, the rate could not exceed 7 percent even though 4.5 percent plus 2.75 percent would imply a rate of 7.25 percent if the mortgage rate increases were not capped.
4. In the mortgage described above, what is the maximum rate you could be charged if the Treasury bill rates rose to 10 percent and stayed there?
Solution: 10 percent—which equals the initial 5 percent rate plus the 5 percent lifetime cap.
DO YOU UNDERSTAND?
1. If you owned a $100,000 security interest in a pass-through mortgage pool that contained $200,000,000 in mortgages and received $20,000,000 in interest payments and $2,000,000 in principal payments in its first year, how much principal and interest would you receive (if there were no mortgage servicing costs) that year?
Solution: You own a 1/2,000 interest in the pool so you receive 1/2,000 of the interest—or $10,000 in interest—plus 1/2,000 of the principal, or $1,000 in principal, since you receive principal and interest on a “pro rata” basis according to your ownership interest in the pool.
2. If your security interest in the mortgage pool described above were a PO, or principal only, security, rather than a regular pass-through security, how much would you have received after the first year?
Solution: $1,000, or a 1/2,000 “pro rata” share of the total principal payments.
3. Why are securitized mortgage-backed securities often more attractive to investors than pass-through securities on the same pool of mortgages would be?
Solution: On some tranches, payments may be more certain or predictable than payments on the mortgage pool as a whole. Conversely, on other tranches, payments may be less certain but promised rates of return are higher. Alternatively, payments on some tranches may be credit-enhanced to reduce their risk; while on other tranches, greater risk is compensated for with higher promised rates of return. In addition, some mortgage pools may be structured so that people who pay high taxes on interest receive only principal repayments, or vice versa. Finally, payments on fixed-interest mortgages may be restructured so some tranches receive variables rates of interest while others receive interest returns that vary inversely with market interest rates. Both types of securities may appeal to different types of investors. Thus, by restructuring payments flow from pools of mortgages, various tranches can be derived that have greater appeal to buyers than the original pool of mortgages and thus can be sold for a higher combined value in the nation’s capital markets.
4. Why is government or private insurance important to the mortgage markets?
Solution: Buyers of mortgages need only check the creditworthiness of the insurer of the mortgages and need not go to the trouble and expense of checking the credit of each individual mortgage borrower in the pool of mortgages that back the mortgage-backed securities or the individual mortgages they are buying.