Chapter 4
History of Real
Estate Finance
and the FixedRate Mortgage
Chapter 4
Learning Objectives
Understand how residential lending
evolved from the earliest of times
through World War II
 Understand the mechanics of the
standard fixed-rate mortgage

History Of Real Estate
Finance

ROMAN LAW
– Transfer of title and possession until
repayment
– No transfer of title or possession. Lender
could take title and possession under
suspicion of default
– No transfer of title or possession. Lender
could take title under actual default
History Of Real Estate
Finance

GERMAN LAW
– Gage is a deposit made to fulfill an
agreement
– Mort is French for Dead. Real property (not
transportable) was a dead gage
– In default the lender could take title but
could not look further for relief
History Of Real Estate
Finance

ENGLISH LAW
– Concept of usury in that charging interest
was sinful
– Equitable Right Of Redemption - Allowing
borrower to redeem the property after
default
History Of Real Estate
Finance



U.S. law is a mix of Roman, German, And
English law
EARLY EXPANSION
– Little need for lending
– Some building societies formed to
consolidate funds for home buying
POST-CIVIL WAR
– Increased mortgage lending to finance
westward expansion
– Typical loan was short-term, interest-only
History Of Real Estate
Finance

Early 1900s through 1920s
– Federal Reserve in 1913 allowed banks to
write 5-year, 50% loan-to-value ratio, nonamortizing mortgages
– Building and Loan Associations expanded
rapidly
– Real estate prices rose rapidly
– After 1929 market crash, real estate prices
dropped dramatically
History Of Real Estate
Finance

1930s
– Market crash in 1929 ushered in the Great
Depression
– Banking system collapsed, money supply
plummeted, unemployment soared
– Refinancing short-term, non-amortizing
loans became a problem
– A number of federal agencies created
including FSLIC (1934), FHA (1934), and
Fannie Mae (1938)
Fixed-Rate Mortgages

PRESENT VALUE OF AN ANNUITY
PVANN =
(1+i)n – 1
(i) (1+i)n
 MORTGAGE CONSTANT
MCi =
(i) (1+i)n
(1+i)n - 1
Fixed-Rate Mortgages

IMPORTANT VARIABLES
– Amount Borrowed
– Contract Interest Rate
– Maturity (Term)
– Outstanding Balance
– Amortization
– Payment
– Financing Costs Including Discount Points
– Annual Percentage Rate (APR)
Fixed-Rate Mortgages

Suppose You Borrow $100,000 @
7.50% For 30 Years, Monthly
Payments
– What Is Your Monthly Payment To Fully
Amortize The Loan Over Its Term?
Fixed-Rate Mortgages
PMT = AMT. BORROWED (MCi,n)
PMT = $100,000 (MC7.5,30)
PMT = $100,000 x
(.075/12) (1+.075/12)360
(1+.075/12)360 – 1
= $100,000 (.0069921)
= $699.21
Fixed-Rate Mortgages

KEYSTROKES FOR PAYMENT CALCULATION
– Enter amount borrowed as negative PV
– Enter the contract rate (adjusted monthly)
– Enter the number of payments
– Solve for payment (PMT)
– Caution: If your calculator is set on one
payment per year, you must divide the
interest rate by 12 and multiply the years
by 12.
Fixed-Rate Mortgages

LOAN AMORTIZATION
– Payment consists of interest and repayment of
principal

AMORTIZATION FOR MONTH ONE
– Payment is $699.21
– Interest portion is $100,000 (.075/12) = $625
– Repayment of principal portion is remainder,
$699.21 - 625 = $74.21
– Each month’s interest is calculated as the loan
balance at the beginning of the month times the
Fixed-Rate Mortgages

OUTSTANDING BALANCE
– Present value of the remaining stream of
payments discounted at the contract rate

FOR OUR EXAMPLE AT THE EOY 5:
– Enter the payment (699.21)
– Enter the contract rate (.075/12)
– Enter the number of remaining payments
(300)
– Solve for present value (PV) ($94,617)
Fixed-Rate Mortgages

Annual Percentage Rate (APR)
– The effective cost of the loan assuming it is
held for its full term
– Some Items Included In APR Calculation:
 Origination Fee, Lender Inspection Fee,
Assumption Fee, Underwriting Fee, Tax
Service Fee, Document Prep Fee,
Prepaid Interest, Mortgage Insurance
Premium, Discount Points
Fixed-Rate Mortgages
Contract Term
Rate
Disc.
Points
APR
PMT @
100,000
5.50%
30 yrs
0.00
5.56%
$567.79
5.375% 30 yrs
1.00
5.705% $559.97
5.25%
30 yrs
2.00
5.534% $552.20
5.125% 30 yrs
2.50
5.42%
$544.49
Fixed-Rate Mortgages
Contract Term
Rate
Disc.
Points
APR
Pmt @
100,000
4.875% 15 yrs
0.00
5.09%
$784.30
4.75%
15 yrs
1.00
5.302% $777.83
4.625% 15 yrs
1.25
4.787% $771.40
Trade Off Between Contract
Rate and Discount Points

Contract Rate
7%
6.75%
6.50%
6.25%

Discount Points
0
1.00
2.875
3.00
Calculating The APR

Assumption: Borrow $100,000 for 30
years, monthly payments
7% & O pts:
100,000 - 0 = $665.30 (PVAFi/12,360)
i =7%
6.75% & 1 pt:
100,000 - 1,000 = $648.60 (PVAFi/12,360)
i = 6.85%
Calculating The APR Cont.
6.50% & 2.875 pts:
100,000-2,875= $632.07 (PVAFi/12,360)
i = 6.78%
6.25% & 3 pts:
100,000-3,000= $615.72(PVAFi/12,360)
i = 6.54%
Calculating the
Effective Cost Under
Shortened Holding Period

Assumption: Borrow $100,000 for 30 years,
monthly payments, hold for five years
7% & 0 pts:
$100,000 - 0 = $665.30 (PVAFi/12,60) +
$94,132 (PVFi/12,60)
i = 7%
6.75% & 1 pt:
$100,000 - $1,000 = $648.60 (PVAFi/12,60) +
$93,876 (PVFi/12,60)
i = 6.99%
Calculating the Effective Cost
Under Shortened Holding Period
6.50% & 2.875 pts:
$100,000 - 2,875 =
$632.07(PVAFi/12,60) + $93,611(PVFi/12,60)
 i = 7.2%
6.25% & 3 pts:
$100,000 - $3,000 = $615.72(PVAFi/12,60)
+ $93,337(PVFi/12,60)
 i = 6.98%
Summary of Effective
Costs

Option
7% & 0 pts
6.75% & 1 pt
6.50% &2.875 pts
6.25% & 3 pts
APR
5 Years
7%
6.85%
6.78%
6.54%
7%
6.99%
7.21%
6.98%
Prepayment Penalty




Assumptions: $100,000 at 7.5% for 30 years,
monthly payments. Five percent prepayment
penalty over entire term. Repay at the end of year 5
PMT = $699.21
BalanceEOY5 = 94,617
Effective cost with no points
$100,000 - 0 =
$699.21(PVAFi/12,60)+$94,617(1.05)(PVFi/12,60)
i = 8.28%
Fifteen Year Mortgage

Borrow $100,000 at 7.50% for 15 years,
monthly payments
PMT15 = $100,000( MC7.5,15) = $927.01
PMT30 = $100,000 (MC7.5,30) = $699.21
Total interest over 15 year term

$927.01(180) - $100,000 = $66,862
Total interest over 30 year term

$699.21(360) - $100,000=$151,716
Difference in interest paid

$151,716 - $66,862 = $84,854
Extra Payment Monthly

PMT= $100,000 (MC7.5,30) = $699.21
$699.21/12= $58.27 Extra paid monthly
New PMT= $699.21 + $58.27 = $757.48
 Number of payments at new payment amount

$100,000 = $757.48 (PVAF7.5/12, n)


n= 279.84, approximately 23 years
Amount saved
$699.21 ( 80.16) - $58.27 (279.84)
$56,049 - $16,306 = $39, 743
Calculating Discount Points
Suppose you borrow $100,000 at 7%
for 30 years, monthly payments. The
APR on the loan is 7.25%. What
amount of points were charged?
 100,000 – pts = 665.30 (PVAF7.25/12, 360)
 100,000 – pts = 97526
 Pts = $2474
 2474/100,000 = 2.47 points

Extra Payment-Lump Sum




PMT= $100,000 ( MC7.5,30) = $699.21
$10,000 Extra paid at the end of year 3
BALEOY3 :
$97,014
Minus extra payment:
$10,000
New balanceEOY3 :
$87,014
Number of payments remaining after extra
payment
$87,014= $699.21 ( PVAF7.5/12, n)


n= 241.41
Amount saved:
$699.21 (82.59) - $10,000= $47,748
Calculating Discount Points w/
a Shortened Holding Period

Suppose you take a FRM for $100,000 at 7%
for 30 years, monthly payments. The effective
cost with a 5-year holding period is 7.375%.
What amount of discount points were
charged?
100,000 – pts = 665.30 (PVAF7.375/12, 60)
+ 94,132 (PVF7.375/12, 60)
100,000 – pts = 98476
pts = $1524 or 1524/100,000 = 1.524 pts
Equalizing APRs
Option 1: $100,000 at 6.5% for 30
years, monthly payments. APR = 6.60%
 Option 2: $100,000 at 6.25% for 30
years, monthly payments. How many
points must be charged to equalize the
APR on the two options?

Equalizing APRs (con’t)
100,000 – pts = 615.72 (PVAF6.60/12, 360)
100,000 – pts = 96,408
Pts = $3,592
Pts = 3,592/100,000 = 3.592 pts
Calculating Financing Fees
Other Than Discount Points

You borrow $100,000 at 6% for 30
years, mthly pmts. You pay 2.50
discount points. Your APR is 6.375%.
What is the amount of your other fees?
100,000 – 2,500 – fees =
599.55 (PVAF6.375/12, 360)
100,000 – 2,500 – fees = 96,102
Other Financing Fees = $1,398
Interest-Only Fixed-Rate
Mortgage




Suppose you take a $140,000, 10/20 interestonly FRM at 7%, monthly payments.
What is the interest-only payment?
Pmt = 140,000 (.07/12) = $816.67
What is the payment for the last 20 years to
fully amortize the loan?
Pmt = 140,000 (MC7, 20) = $1085.42
What is the balance at the EOY20?
BalEOY20 = 1085.42 (PVAF7/12, 120) = $93,483