1
Chapter 14
2
After completing this chapter, you will be able
to
the principal balance after any payment
using both the Prospective Method
and the Retrospective Method
LO 1.
the final loan payment when it differs
from the others
LO 2.
LO 3.
the principal and interest components of
any payment
And
3
LO 4.
mortgage payments for the initial loan and its
renewals
mortgage loan balances and amortization periods
to reflect prepayments of principal
LO 5.
4
Q
A 20,000 mortgage loan at 9
compounded monthly requires monthly payments
during its 20-year amortization period.
LO 1.
(1) Calculate the monthly payment.
(2) Using the
monthly payment from part (1),
calculate the PV of all payments.

(3) Why does the answer in (2) differ from
20,000?
n 12 20 240
PV 20000
FV 0
1.
PMT -179.95
240
20 000
9
0
2.

3.
5
2.
n 1220 240
PV ?
FV 0
PMT 179.95
179.95
PV 20,000.5345
179.95
3.
The difference of 0.5345 is due to rounding the
monthly payment to the nearest cent!
6
Calculate the exact balance after 5 years
assuming the final payment will be adjusted for
the effect of rounding the regular payment.
Now
Calculate the exact n for monthly payments of
179.95 to repay a 20,000 loan...
20 000
N 239.982
7
Calculate the exact balance after 5 years
assuming the final payment will be adjusted for
the effect of rounding the regular payment.
Now
N 179.9821
P/V 17,741.05
After 5 years, 239.982 60 179.982 payments
remain. Therefore, balance (after 5 years)
PV
of 179.982 payments of 179.95
60
8
Consider that
An Original Loan
The PV of ALL of the Payments
(discounted at the contractual rate of interest
on the loan)
Also, that
A Balance
The PV of the remaining Payments
(discounted at the contractual rate of interest
on the loan)
Then
9
this can be expressed as the Statement of
Economic Equivalence
For a focal date of the original date of the loan,
(Original Loan)
Focal Date
10

of the xth payment, the Statement
of Economic Equivalence becomes
Suppose we locate the
Focal Date
Balance
This is now rearranged to isolate the Balance
Balance
11
Prospective Method for Loan Balances
is based on PAYMENTS YET to be MADE!
whereas
is based on PAYMENTS ALREADY MADE!
12
Q
A 20,000 mortgage loan at 9
compounded monthly requires monthly payments of
179.95 during its 20-year amortization period.
Calculate the exact balance after 5 years.
Solve using
Retrospective Method
Prospective Method
Then compare
13
Q
A 20,000 mortgage loan at 9
compounded monthly requires monthly payments of
179.95 during its 20-year amortization period.
Calculate the exact balance after 5 years.
Balance FV of 20,000 FV of first 60 payments
FV 17,741.05
60
179.95
9
20,000
14
Q
A 20,000 mortgage loan at 9
compounded monthly requires monthly payments of
179.95 during its 20-year amortization period.
Calculate the exact balance after 5 years.
12 20 Years 240
Total payments
- 60 made 180 remaining
Balance PV of remaining 180 payments
PV 17,741.88
180
179.95
9
0
15
Comparison of Methods
Difference (0.83) is because the Prospective
Method assumes that the
final payment is the same as all the others.
The Retrospective Method is based on
payments already made.
16
Q
A 20,000 mortgage loan at 9
compounded monthly requires monthly payments of
179.95 during its 20-year amortization period.
LO 2.
Calculate the size of the final payment.
Final Payment (1i) (Balance after 2nd to
last payment)
Balance after 239 payments FV of 20,000 after
239 months FV of 239 payments
179.95
FV - 175.42
239
9
20,000
Final Payment (10.09/12) 175.42
176.74
17
Q
Meditech Laboratories borrowed 28,000 at
10, compounded quarterly,
to purchase new testing equipment.
Payments of 1,500 are made every
3 months. A. Calculate the balance after the 10th
payment. B. Calculate the final payment.
A.
Balance after 10 payments FV of 28,000 after
10 quarters FV of 10 payments
FV - 19,037.29
10
1500
10
28,000
B.
18
B. Calculate the final payment.
N 25.457
FV -673.79
0
25
19
Final Payment (10.10/4) 673.79
690.63
20
LO 3.
A 9,500 personal loan at 10.5
compounded monthly is to be repaid over a
4-year term by equal monthly payments. A.
Calculate the interest and principal components
of the 29th payment. B. How much interest will
be paid in the second year of the loan?
21
First find the size of the monthly payment
9500
PV
n
i
12(4) 48
.105/12
PMT - 243.23
48
10.5
9500
0
22
First find the balance after the 28 payments
A.
PMT - 243.23
FV -4445.06
28
243.23
Interest Component of Payment 29
i Balance after 28th payment
0.105/12 4445.06
38.89
Principal Component PMT Interest Component
243.23 - 38.89
204.34
23
First find the balance after 1 Year, and the
balance after 2 Years
B.
FV -7483.53
FV -5244.84
12
24
Total Principal paid in year 2 7,483.53 -
5,244.84
2,238.69
Total Interest paid in year 2 12(243.23) -
2,238.69
680.07
24
Mortgage
is a loan
secured by some physical
property
25
the borrower is called the
mortgagor
the lender is called the mortgagee
...and
26
Face Value of mortgage original principal amount
Term
From date on which loan advanced To date on
which the remaining
Principal Balance is due and payable

most common periods are 20 and 25 years.
Interest Rate
usually a lender will commit to a
fixed interest rate for only a shorter period or
term (6 months to 7 years)
27
A Mortgage Loan at 8.5 compounded semiannually
with a 25-year amortization
period
28
The Composition of Mortgage Payments during a

25-year Amortization
Approximately 40
Approximately 60
Year 14
29
Mortgages Declining Balance during a

25-year Amortization
Principal declines slower in
earlier years
30
Qualifying for One
31
Loan-to-Value Ratio (LVR)
Gross Debt Service Ratio (GDS)
Total Debt Service Ratio (TDS)
32
Loan-to-Value Ratio (LVR)
x
Principal Amount of Loan

75
100
Lending Value of Property
Gross Debt Service Ratio (GDS)
Total monthly payments for Mortgage, Property
taxes, and Heat
x

32
100
Gross Monthly Income
Total Debt Service Ratio (TDS)
Total monthly payments for Mortgage, Property
taxes, Heat and Other Debts
x

40
100
Gross Monthly Income
33
You have saved 35,000 for the down payment

on a home. You want to know the

maximum conventional mortgage loan
for
which you can qualify in order
to determine the highest
price you can pay for a home.
gross monthly income is 3,200 18 payments of
300 per month remaining on a car loan
property taxes of 150 per month and heating
costs of 100 per month the bank has upper
limits of 32 for the GDS Ratio and 40 for the
TDS Ratio
Personal Data
What maximum monthly mortgage payment do the GDS
and TDS ratios permit?
34
Gross Debt Service Ratio (GDS)
Maximum Mortgage payment 150 100

32
3,200
Maximum Mortgage payment .32(3200) - 250

774
35
Total Debt Service Ratio (TDS)
Maximum mortgage payment 150 100 300

40
3,200
Maximum Mortgage payment .40(3200) - 550

730
36
Q
What is the maximum mortgage
for which you qualify?
Use a 25-year
amortization and an interest
rate of 8 compounded semiannually for a
five-year term.
12
P/Y 12
C/Y 2
0
P/V 95,648.21
8
0
2
730
300
37
Q
Based on a 35,00 down payment and the
maximum loan possible, what is the highest price
you can pay for a home?
Loan-to-Value Ratio (LVR)

95, 600
75
Minimum house value

95, 648

127,530.67
Minimum house value
75
...and
38
At this price, the minimum down payment is
127,531 95,648 31,883
the maximum price you can afford to pay for a
home is
127, 531 130,649
3,118
39
Common Prepayment
40
Limited penalty-free prepayment
No restrictions or penalties on extra
payments by the borrower!
No prepayment without a
penalty
Lump or Balloon Payments
10 or 15 of the original amount
Increasing the Regular Paymentpermanently
Once a year by 10 or 15
Double-Up
Pay twice the amount for any monthly payment
41
The most common prepayment penalty is the greater
of
Contract provides for a financial penalty on any
prepayment not specifically permitted
Three months interest on the amount prepaid, or
The lenders reduction in interest revenue from
the prepaid amount
(over the remainder of the
mortgages term)
42
The interest rate for the first 5-year term of
a 100,000 mortgage loan is 7.5 compounded
semiannually. The mortgage requires monthly
payments
over a 25 year amortization period. The mortgage
contract gives the borrower the right to prepay
up to 10 of the original mortgage loan,
once a year, without interest penalty. Suppose
that, at the end of the second year of the
mortgage, the borrower makes a
prepayment of 10,000.
LO 4.
LO 5.

1. How much will the amortization period be
   shortened?
2. What will be the principal balance
   at the end of
   the five-year term?
   

43
the payments based on a 25-year amortization
1.
2.
the balance after 24 payments
- Reduce this balance by 10,000
3.
the number of monthly payments needed
to pay off this new balance
4.
the reduction in the original 25-year
amortization period
5.
44
c
PV
n
i
100,000
2512 300
.075/2
2/12
PMT -731.55
12
100,000
2
300
7.5
0
45
87,007.25
FV -97,007.25
731.55
24
10,000
46
N 214.60
87,007.25
0
with the prepayment 24 215 239 Total
payments Therefore, 300-239 61 months saved...
i.e. 5 yrs 1 month
47
Interactive Mortgage Payoff Chartonline
www.mcgrawhill.ca/college/jerome/
Click On
Click On
Click On
Select
-or-
48
This completes Chapter 14