1a. A property is purchased for $70,000. The purchase is financed with a GPM carrying a 12 percent interest rate. A 7.5 percent rate of graduation will be applied to monthly payments beginning each year after the loan is originated for a period of five years. The initial loan amount is $63,000 for a term of 30 years. The homeowner expects to sell the property after seven years.
a.If the initial monthly payment is $498.57, what will payments be at the beginning of years 2, 3, 4, and 5?
b.What would the payment be if a CPM loan was available?
c.Assume the loan is originated with two discount points. What is the effective yield on the GPM?
1b. Why do level or constant monthly mortgage payments increase so sharply during periods of inflation? What does the tilt effect have to do with this?
1c. A borrower obtains a fully amortizing CPM loan for $125,000 at 11 percent interest for 10 years. What will be the monthly payment on the loan? If this loan had a maturity of 30 years, what would be the monthly payment?
1d. What are the major differences between the CAM, and CPM loans? What are the advantages to borrowers and risks to lenders for each? What elements do each of the loans have in common?
2a. Mr. Qualify is applying for a $100,000 GPM loan for 25 years at an interest rate of 9 percent. Payments would be designed so as to graduate at the rate of 7.5 percent for three years beginning with payments in the second year.
a.What would monthly payments be for Mr. Qualify in each of the first five years of the loan?
b.What would the loan balance be on the GPM at the end of year 3?
c.If the lender charged 4 points at origination, what would be the effective interest rate on this loan after five years?
2b.As inflation increases, the impact of the tilt effect is said to become even more burdensome on borrowers. Why is this so?
2c. A fully amortizing mortgage loan is made for $80,000 at 6 percent interest for 25 years. Payments are to be made monthly. Calculate:
b.Interest and principal payments during month 1.
c.Total principal and total interest paid over 25 years.
d.The outstanding loan balance if the loan is repaid at the end of year 10.
e.Total monthly interest and principal payments through year 10.
f.What would the breakdown of interest and principal be during month 50?
2d. Define amortization.List the five types discussed in this chapter.
3a.Excel. Refer to the “Ch4 GPM” tab in the Excel Workbook provided on the Web site. How would the initial payment change if the payments increase by 5 percent each year instead of 7.5 percent?
3b.A fully amortizing mortgage loan is made for $100,000 at 6 percent interest for 30 years. Determine payments for each of the periods a–d below if interest is accured:
3c. Why do the monthly payments in the beginning months of a CPM loan contain a higher proportion of interest than principal repayment?
4a. Regarding Problem 3, how much total interest and principal would be paid over the entire 30-year life of the mortgage in each case? Which payment pattern would have the greatest total amount of interest over the 30-year term of the loan? Why?
(Reference Problem 3)
A fully amortizing mortgage loan is made for $100,000 at 6 percent interest for 30 years. Determine payments for each of the periods a–d below if interest is accured:
4b.What are loan closing costs? How can they be categorized? Which of the categories influence borrowing costs and why?
5a. A fully amortizing mortgage loan is made for $100,000 at 6 percent interest for 20 years.
a.Calculate the monthly payment for a CPM loan.
b.What will the total of payments be for the entire 20-year period? Of this total, how much will be interest?
c.Assume the loan is repaid at the end of 8 years. What will be the outstanding balance? How much total interest will have been collected by then?
d.The borrower now chooses to reduce the loan balance by $5,000 at the end of year 8.
(1) What will be the new loan maturity assuming that loan payments are not reduced?
(2) Assume the loan maturity will not be reduced. What will the new payments be?
5b.In the absence of loan fees, does repaying a loan early ever affect the actual or true interest cost to the borrower?
6a. A 30-year fully amortizing mortgage loan was made 10 years ago for $75,000 at 6 percent interest. The borrower would like to prepay the mortgage balance by $10,000.
a.Assuming he can reduce his monthly mortgage payments, what is the new mortgage payment?
b.Assuming the loan maturity is shortened and using the original monthly payments, what is the new loan maturity?
6b. Why do lenders charge origination fees, especially loan discount fees?
7a. A fully amortizing mortgage is made for $100,000 at 6.5 percent interest. If the monthly payments are $1,000 per month, when will the loan be repaid?
7b.What is the connection between the Truth-in-Lending Act and the annual percentage rate (APR)?
8a. A fully amortizing mortgage is made for $80,000 for 25 years. Total monthly payments will be $900 per month. What is the interest rate on the loan?
8b.What is the effective borrowing cost (rate)?
9a. A partially amortizing mortgage is made for $60,000 for a term of 10 years. The borrower and lender agree that a balance of $20,000 will remain and be repaid as a lump sum at that time.
a.If the interest rate is 7 percent, what must monthly payments be over the 10-year period?
b.If the borrower chooses to repay the loan after 5 years instead of at the end of year 10, what must the loan balance be?
9b. What is meant by the “nominal rate” on a mortgage loan?
10a. An “interest only” mortgage is made for $80,000 at 10 percent interest for 10 years. The lender and borrower agree that monthly payments will be constant and will require no loan amortization.
a.What will the monthly payments be?
b.What will be the loan balance after 5 years?
c.If the loan is repaid after 5 years, what will be the yield to the lender?
d.Instead of being repaid after 5 years, what will be the yield if the loan is repaid after 10 years?
10b.What is the accrual rate and payment rate on a mortgage loan? happens when the two are different?
11a. A partially amortizing loan for $90,000 for 10 years is made at 6 percent interest. The lender and borrower agree that payments will be monthly and that a balance of $20,000 will remain and be repaid at the end of year 10. Assuming 2 points are charged by the lender, what will be the yield if the loan is repaid at the end of year 10? What must the loan balance be if it is repaid after year 4? What will be the yield to the lender if the loan is repaid at the end of year 4?
11b.An expected inflation premium is said to be part of the interest rate, what does this mean?
12a. A loan for $50,000 is made for 10 years at 8 percent interest and no monthly payments are scheduled.
a.How much will be due at the end of 10 years?
b.What will be the yield to the lender if it is repaid after 8 years? (Assume monthly compounding.)
c. If 1 point is charged in (b) what will be the yield to the lender?
12b.A mortgage loan is made to Mr. Jones for $30,000 at 10 percent interest for 20 years. If Mr. Jones has a choice between a CPM and a CAM, which one would result in his paying a greater amount of total interest over the life of the mortgage? Would one of these mortgages be likely to have a higher interest rate than the other? Explain your answer.
13a. John wants to buy a property for $105,000 and wants an 80 percent loan for $84,000. A lender indicates that a fully amortizing loan can be obtained for 30 years (360 months) at 8 percent interest; however, a loan origination fee of $3,500 will also be necessary for John to obtain the loan.
a.How much will the lender actually disburse?
b.What is the effective interest rate for the borrower, assuming that the mortgage is paid off after 30 years (full term)?
c.If John pays off the loan after five years, what is the effective interest rate? Why is it different from the effective interest rate in (b)?
d.Assume the lender also imposes a prepayment penalty of 2 percent of the outstanding loan balance if the loan is repaid within eight years of closing. If John repays the loan after five years with the prepayment penalty, what is the effective interest rate?
13b.What is negative amortization?
14a. A lender is considering what terms to allow on a loan. Current market terms are 8 percent interest for 25 years for a fully amortizing loan. The borrower, Rich, has requested a loan of $100,000. The lender believes that extra credit analysis and careful loan control will have to be exercised because Rich has never borrowed such a large sum before. In addition, the lender expects that market rates will move upward very soon, perhaps even before the loan is closed. To be on the safe side, the lender decides to extend to Rich a CPM loan commitment for $95,000 at 9 percent interest for 25 years; however, the lender wants to charge a loan origination fee to make the mortgage loan yield 10 percent. What origination fee should the lender charge? What fee should be charged if it is expected that the loan will be repaid after 10 years?
14b.What is partial amortization?
15.A borrower is faced with choosing between two loans. Loan A is available for $75,000 at 6 percent interest for 30 years, with 6 points to be included in closing costs. Loan B would be made for the same amount, but for 7 percent interest for 30 years, with 2 points to be included in the closing costs. Both loans will be fully amortizing.
a.If the loan is repaid after 20 years, which loan would be the better choice?
b. If the loan is repaid after five years, which loan is the better choice?
16.A reverse annuity mortgage is made with a balance not to exceed $300,000 on a property now valued at $700,000. The loan calls for monthly payments to be made to the borrower for 120 months at an interest rate of 11 percent.
a.What will the monthly payments be?
b.What will be the RAM balance at the end of year 3?
c.Assume that the borrower must have monthly draws of $2,000 for the first 50 months of the loan. Remaining draws from months 51 to 120 must be determined so that the $300,000 maximum is not exceeded in month 120. What will draws by the borrower be during months 51 to 120?
17.A borrower and lender agree on a $200,000 loan at 10 percent interest. An amortization schedule of 25 years has been agreed on; however, the lender has the option to “call” the loan after 5 years. If called, how much will have to be paid by the borrower at the end of 5 years?
18.A fully amortizing CAM loan is made for $125,000 at 11 percent interest for 20 years.
a.What will be the payments and balances for the first 6 months?
b.What would payments be for a CPM loan?
c.If both loans were repaid at the end of year 5, would the lender earn a higher rate of interest on either loan?
19.A $50,000 interest only mortgage loan is made for 30 years at a nominal interest rate of 6 percent. Interest is to be accrued daily, but payments are to be made monthly.
a.What will the monthly payments be on such a loan?
b.What will the loan balance be at the end of 30 years?
c.What is the equivalent annual rate on this loan?
20.Comprehensive Review Problem: A mortgage loan in the amount of $100,000 is made at 12 percent interest for 20 years. Payments are to be monthly in each part of this problem.
a.What will monthly payments be if:
(1) The loan is fully amortizing?
(2) It is partially amortizing and a balloon payment of $50,000 is scheduled at the end of year 20?
(3) It is a nonamortizing, or “interest only,” loan?
(4) It is a negative amortizing loan and the loan balance will be $150,000 at the end of year 20?
b.What will the loan balance be at the end of year 5 under parts a (1) through a (4)?
c.What would be the interest portion of the payment scheduled for payment at the end of month 61 for each case (1) thru (4) above?
d.Assume that the lender charges 3 points to close the loans in parts a (1) through a (4). What would be the APR for each?
e.If the loan is prepaid at the end of year 5, what will be the effective rate of interest for each loan in parts a (1) – a (4) ?
f.Assume conditions in a (1) except that payments will be “interest only” for the first 3 years (36 months). If the loan is to fully amortize over the remaining 17 years, what must the monthly payments be from year 4 through year 20? g. Refer to a (4) above, where the borrower and lender agree that the loan balance of $150,000 will be payable at the end of year 20:
(1) How much total interest will be paid from all payments? How much total amortization will be paid?
(2) What will be the loan balance at the end of year 3?
(3) If the loan is repaid at the end of year 3, what will be the effective rate of interest?
(4) If the lender charges 4 points to make this loan, what will the effective rate of interest be if the loan is repaid at the end of year 3?
21.Excel. Refer to the “Ch4 Eff Cost” tab in the Excel Workbook provided on the Web site. Suppose another loan is available that is an 11 percent interest rate with 6 points. What is the effective cost of this loan compared to the original example on the template?
22.Excel. Refer to the “Ch4 GPM” tab in the Excel Workbook provided on the Web site. How would the loan balance at the end of year 7 change if the payments increase by 5 percent each year instead of 7.5 percent?