Chapter 4
Fixed Rate Mortgage Loans
1
Overview
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Mortgage Interest Rates
Components of the Mortgage Interest Rate
Constant Amortization Mortgage (CAM)
Constant Payment Mortgage (CPM)
CAM and CPM Payment Patterns
Computing a Loan Balance
Loan Closing Costs
Pricing a Loan
Other Loan Patterns
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Partially Amortizing Loan
Negative Amortization
Option Mortgages
Reverse Annuity Mortgage (RAM)
2
Mortgage Interest Rates
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What will borrowers pay for the use of
funds?
What are lenders willing to accept for
the use of funds?
Housing Demand Factors: Income &
Demographics
Mortgage Funds Supply Factors:
Alternative Investments
3
Components of the Mortgage
Interest Rate
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Real Rate of Interest
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Time Preference for Consumption
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Production Opportunities in the Economy
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Compensation to delay a purchase
Competition for funds when there are other
investment opportunities
Inflation Expectation
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Retain purchasing power
4
Components of the Mortgage
Interest Rate – Continued
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Default Risk
Interest Rate Risk
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Anticipated Inflation and Unanticipated
Inflation
Prepayment Risk
Liquidity Risk
Legislative Risk
5
Components of the Mortgage
Interest Rate – Continued
it  r1  p1  f1
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r = Real Rate
f1 = Inflation Rate
p1 = Risk Premiums
6
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Ending
Balance
$59,833.33
$59,666.67
$59,500.00
$59,333.33
$59,166.67
$59,000.00
$500.00
$333.33
$166.67
$0.00
Amortization = Original Loan Balance / Number of Payments
Monthly Payment = Interest + Amortization
Ending Balance = Opening Balance – Amortization
$166.67
$166.67
$166.67
$166.67
$166.67
$166.67
$166.67
$166.67
$166.67
$166.67
$60,000.00
Monthly
Payment
$766.67
$765.00
$763.33
$761.67
$760.00
$758.33
$173.33
$171.67
$170.00
$168.33

$600.00
$598.33
$596.67
$595.00
$593.33
$591.67
$6.67
$5.00
$3.33
$1.67
Amortization
Periodic Rate = Annual Rate / Payment per Year
Interest
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1
2
3
4
5
6
357
358
359
360
Total
Opening
Balance
$60,000.00
$59,833.33
$59,666.67
$59,500.00
$59,333.33
$59,166.67
$666.67
$500.00
$333.33
$166.67
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Month
$60,000.00
12.00%
30
12
360
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Loan Amount
Interest Rate
Loan Term
Payment per Year
Number of Payments
Opening Balance = Previous Period Ending Balance
Interest = Opening Balance × Periodic Rate
Constant Amortization
Mortgage (CAM)
7
Constant Amortization Mortgage
Interest
Amortization
Monthly Payment
$900.00
$800.00
$700.00
Amount ($)
$600.00
$500.00
$400.00
$300.00
$200.00
$100.00
$0.00
0
12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300 312 324 336 348 360
Month
8
Constant Payment Mortgage
(CPM)
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FRM payments are structured as an ordinary annuity
PV of the annuity is the amount borrowed
The monthly payment on a 30-year, 12%, $60,000 loan is:
N
I/Y
P/Y
PV
PMT
FV
360
12
12
-60,000
617.17
0
MODE
Notes:
 To get the answer press CPT and then what you are trying to get
 To clear the calculator memory use 2nd CLR TVM
 To change P/Y, press 2nd P/Y, enter the amount and press ENTER.
To get out of this mode use 2nd QUIT
 Annuity due setting is BGN (for beginning): 2nd BGN, 2nd SET, 2nd
QUIT
9
Amortization = Monthly Payment – Interest
Ending Loan Balance = Beginning Loan Balance –
Amortization
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Periodic Rate = Annual Rate / Payment per Year
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Ending
Loan
Balance
$59,982.83
$59,965.49
$59,947.98
$59,930.29
$59,912.43
$59,894.38
$1,815.08
$1,216.06
$611.06
$0.00
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Loan Amount
$60,000.00
Interest Rate
12.00%
Loan Term
30
Payment per Year
12
Number of Payments
360
Monthly Payment
$617.17
Beginning
Monthly
Month
Loan
Interest
Amortization
Payment
Balance
1
$60,000.00
$617.17
$600.00
$17.17
2
$59,982.83
$617.17
$599.83
$17.34
3
$59,965.49
$617.17
$599.65
$17.51
4
$59,947.98
$617.17
$599.48
$17.69
5
$59,930.29
$617.17
$599.30
$17.86
6
$59,912.43
$617.17
$599.12
$18.04
357
$2,408.17
$617.17
$24.08
$593.09
358
$1,815.08
$617.17
$18.15
$599.02
359
$1,216.06
$617.17
$12.16
$605.01
360
$611.06
$617.17
$6.11
$611.06
Total
$60,000.00
Beginning Loan Balance = Previous Period Ending Balance
Monthly Payment = Determined using Excel’s PMT function
Interest = Beginning Loan Balance × Periodic Rate
Constant Payment Mortgage
(CPM) – Continued
10
Constant Payment Mortgage
Monthly Payment
Interest
Amortization
$700.00
$600.00
Amount ($)
$500.00
$400.00
$300.00
$200.00
$100.00
$0.00
0
12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300 312 324 336 348 360
Month
11
Constant Amortization/Payment Balances
$60,000.00
$50,000.00
Amount ($)
$40,000.00
$30,000.00
$20,000.00
$10,000.00
$0.00
0
12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300 312 324 336 348 360
Month
12
CAM and CPM Payment
Patterns
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Comparing the CAM & CPM
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Higher initial monthly payments for the CAM
More difficult for a borrower to qualify for a
loan
Amortization of CPM is slower than CAM
CAM payment declines over time
13
Computing a Loan Balance
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The outstanding loan balance is the PV of the
remaining loan payments discounted at the original
loan rate
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After computing the PMT of the original loan just change
N to number of remaining payments then CPT PV
Alternatively, to determine the outstanding balance
of the loan in the previous example after 10 years:
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Compute PMT (617.17)
2nd AMORT
120 ENTER
120 ENTER This will allow you to see
loan information (self explanatory) at that point in time
You can change P1 and P2 to get the data for the
specified payment range
14
Computing Payment
Components
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How much interest do you pay during the
second year?
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How much principal do you pay during the
second year?
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$7,160.67
$245.34
What is the interest component of 72nd
payment?
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$582.37
15
Loan Closing Costs
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There are three categories of loan closing costs:
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Statutory Costs: These charges are associated with the
legal transfer of title and other fees. They are paid for
services by governmental agencies
Third Party Charges: Payments for legal fees,
appraisals, surveys, inspection, and title insurance
Additional Finance Charges: These charges provide
additional income to the lender and therefore should be
included as a part of cost of borrowing
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Loan Origination Fees
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Cover origination expenses
Loan Discount Fees – “Points”
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Used to raise the yield on the loan
Borrower trade-off: points vs. contract rate
1 Point = 1% of the loan amount
16
Loan Closing Costs –
Continued
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Why Points?
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Sticky mortgage rates
Price in the risk of a borrower
Early repayment of a loan does not allow
recovery of origination costs
Earn a profit on loans sold to investors at a
yield equal to the loan interest rate
17
Loan Closing Costs –
Continued
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If there are fees and points, then the effective interest cost is higher
If the previous loan has 3 points, then the lender will disburse: [60,000 –
(60,000 X 0.03)] = –58,200
Loan payments are based on $60,000 and the borrower receives less,
increasing the return to lender
Note that fees and points work the same way
We also assume that the loan is not prepaid
Lenders are required to disclose by law (Truth-in-Lending Act) an annual
percentage rate (APR) computed in a similar manner
The effective interest cost is
N
I/Y
P/Y
PV
PMT
FV
360
12.41
12
-58,200
617.17
0
MODE
18
Loan Closing Costs and
Prepayment
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What would be effective interest cost if the loan is paid early
Assume that after 5 years (60 payments), the loan is paid off
We need to determine the outstanding balance of the loan after 60
payments
Make sure that calculator has the original loan data without fees and
points
2nd AMORT
60 ENTER 60 ENTER
This will allow you to see loan information
at that point in time (58,598.16)
Loan balance becomes an entry for future value
N
I/Y
P/Y
PV
PMT
FV
60
12.82
12
-58,200
617.17
58,598.16
MODE
19
Loan Closing Costs and
Prepayment Penalty
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What would be effective interest cost if the loan is paid early
Assume that after 5 years (60 payments), the loan is paid off
We need to determine the outstanding balance of the loan after 60
payments
Make sure that calculator has the original loan data without fees and
points
2nd AMORT
60 ENTER 60 ENTER
This will allow you to see loan information
at that point in time (58,598.16)
Apply 3% prepayment penalty [58,598.16 × (1 + 0.03) = 60,356]
Loan balance becomes an entry for future value
N
I/Y
P/Y
PV
PMT
FV
60
13.25
12
-58,200
617.17
60,356
MODE
20
Yield and Prepayment Time
Effective Costs Year 1 - 30
6.50%, 0.000 Points
9.00%
8.50%
APR
8.00%
7.50%
7.00%
6.50%
6.00%
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15 16
Year
17
18
19
20
21
22
23
24
25
26
27
28
29
30
21
Pricing a Loan
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How can a lender earn 13% return on a 12% interest rate, 30-year fixed
rate mortgage that is expected to prepay in 10 years?
This is same as asking for points to be charged to achieve the desired
yield
Payment on the loan:
N
I/Y
P/Y
PV
PMT
FV
360
12
12
-1
0.010286
0
MODE
Balance of the loan after 120 payments: 0.934180
PV of payments to lender at the desired return:
N
I/Y
P/Y
PV
120
13
12
-0.9453
PMT
FV
MODE
0.010286 0.934180
The fees should total 100% - 94.53% = 5.47%
22
Partially Amortizing Loan
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What is the payment on a $60,000 loan with 12%
interest rate, 30-year term, monthly payments,
and $40,000 balloon payment at maturity?
N
I/Y
P/Y
PV
PMT
FV
360
12
12
-60,000
605.72
40,000
MODE
23
Negative Amortization
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What is the payment on a $60,000 loan with 12%
interest rate, 30-year term, and monthly
payments?
N
I/Y
P/Y
PV
PMT
FV
360
12
12
-60,000
617.17
0
MODE
What is the balance of this loan if the lender and
borrower agree on a monthly payment of $400
rather than $617.17 after 5 years?
N
I/Y
P/Y
PV
PMT
FV
60
12
12
-60,000
400.00
76,334
MODE
24
Option Mortgages
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In a simple case, a borrower pays interest only for a certain period and
then converts the loan into a fixed rate fully amortizing loan
What is the interest only payment for the first ten years on a $60,000
loan with 12% interest rate, 30-year term, and monthly payments?
N
I/Y
P/Y
PV
PMT
FV
120
12
12
-60,000
600.00
60,000
MODE
What is the monthly payment when the loan converts into a fixed rate
fully amortizing loan?
N
I/Y
P/Y
PV
PMT
FV
240
12
12
-60,000
660.65
0
MODE
25
Reverse Annuity Mortgage
(RAM)
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A RAM is a raising debt falling equity mortgage
It requires large payment later in its life
It is designed for retired home owners who have
little debt on their home
It allows owners to take out equity
What is the payment on a $250,000 RAM with 10%
interest rate, 10-year term, monthly payments?
N
I/Y
P/Y
PV
120
10
12
0
PMT
FV
MODE
1,220.44 -250,000
26
Three Loans when LTV < 20%
1. Conventional
loan with PMI
2. First and
second
loan
3. FHA
insurance
27
Not So Special Specials
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A land developer purchases land, or purchases on option on
land, with the intention of developing or enhancing the
value of the property through improvements
With an option the developer ties up less cash than with an
outright purchase. A developer may be able to “control”
property worth many millions of dollars with an option that
may cost only in the thousands
The developer makes a profit not through the appreciation
in the value of the land but through the value added from
the improvements
28
Not So Special Specials –
Continued
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Zoning compliance – making sure that there are no legal restrictions
to the type of development that is contemplated. If there are, then
efforts must be made to have the zoning changed if possible, or the
development modified to meet the existing zoning regulations
Engineering and surveying – specialists in this field must be
employed to make sure that the types of structures that are
contemplated can be built on the land. The land may have to be
modified to accommodate certain types of structures. In extreme
cases it may be impossible to build certain types of structures on the
available land
Subdividing – the large land parcel is divided into smaller parcels.
The smaller parcels are sold to other developers or to the final
consumer who, in turn, constructs a structure
Physical work – the actual grading of the land, landscaping,
installation of utilities, and so forth
29
Authority to Assess Specially
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Why a city would get into this type of an activity?
30
Specials Example and
Computations
31
Specials Computations
32