# Mortgages Standard and Alternative代寫

• 4.0
4.1  Mortgage Maths: a review
4.2  Standard mortgages: FRM
4.2.2 Interest rate risk
4.3  Alternative mortgage instruments:        4.3.1 ARM
4.3.2  Interest only ARM
4.3.3  Reverse mortgage

Announcements
•Where we are….
•Learning Objectives
LO#4 Explain the characteristics of various mortgage instruments
LO#5 Solve problems related to real estate mortgages
•Main text, pp 97–126
•Class Activity #1
•If you were borrowing to purchase a house, would you prefer a fixed rate interest or variable?
•4.1 Mortgage Maths: a Review
Interest Only Loans
•Principal does not reduce during term of loan; repaid towards the end (5, 10 years)
•Payments are less than amortising loans
•Class Activity #2
Principal = \$382,000, monthly pay @8% pa, 5 years
–Loan repayment = loan amount x interest rate per period
Working (in class)
Amortising loans: Annual

PMT =  L x    i
1 - (1+i)-n
Where,
PMT = loan (re)payment amount per period
L = loan or principal amount
i = interest rate
n = number of periods

•Class Activity #3
Principal = \$382,000, monthly pay @8% pa, 15 years
Working (in class)

Alternatively,
PMT = PV of annuity x mortgage constant
Mortgage constant:
Mci,n =       (i) (1+i)
(1+i)n – 1

•Class Activity #4
Principal = \$382,000, monthly pay @8% pa, 15 years
PMT using alternative formula:
Amortising loans: Monthly
PMT =  L x    i/m
1 - (1+i/m)-nm

Where, m = number of periods pa

•Class Activity #5
Principal = \$382,000, monthly pay @8% pa, 15 years
PMT = ?
Alternatively,
Mci,n =       (i/m) (1+i/m)n*m
(1+i/m)n*m – 1

PMT = ?
•Class Activity #6
Principal = \$382,000, monthly pay @8% pa, 15 years
PMT using alternative formula:

The outstanding loan/amount

OL = PMT x  1-(1+i)-N
i

•Class Activity #7
Principal = \$382,000, monthly pay @8% pa, 15 years
OL after 5 years = ?

–Amortisation schedule
Øsee Excel example
Ø

Ø
•4.2 Standard Mortgages: FRM
•Important variables
–Amount borrowed
–Contract interest rate
–Maturity (term)
–Outstanding balance
–Amortization
–Payment
–Financing costs including discount points
–Annual percentage rate (APR)

•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
•4.2.1 Interest Rate Risk
\$100,000 fixed-rate mortgage @ 8% for 30 years,
PMT = \$100,000 ( MC8,30) = \$733.76
•If the market rate immediately increases to 10%, the market value of this mortgage falls to:
PV = \$733.76 (PVAF10/12,360) = \$83,613
•Lender loses \$16,387

•If the lender can adjust the contract rate to the market rate (10%), the payment increases and the market value of the loan stays constant:
PMT = \$100,000 (MC10,30) = \$877.57
PV = \$877.57 (PVAF10/12,360) = \$100,000
•4.3 Alternative Mortgage Instruments
•Shared Appreciation Mortgage (SAM)
•Reverse Annuity Mortgage (RAM)
•Pledged-Account Mortgage or Flexible Loan Insurance Program (FLIP)
•Designed to solve interest rate risk problem
•Allows the lender to adjust the contract interest rate periodically to reflect changes in market interest rates
•This change in the rate is generally reflected by a change in the monthly payment
•Provisions to limit rate changes
•Initial rate is generally less than FRM rate
ARM Variables
•Index
•Margin
•Interest Rate Caps
–Periodic
•Convertibility
•Negative Amortization
•Teaser Rate
•4.3.2 Interest-Only ARM
•Payment in the initial period is interest-only with no repayment of principal
•After the initial period the loan becomes fully amortizing
•Loan is designed to fully amortize over its stated term
•E.g. A 3/1 Interest-Only ARM is interest-only for the first three years and then becomes a fully amortizing one-year ARM
•4.3.3 Reverse Mortgage
Typical Mortgage - Borrower receives a lump sum up front and repays in a series of payments

Reverse Mortgage - Borrower receives a series of payments and repays in a lump sum at some future time
Typical Mortgage - “ Falling Debt, Rising Equity”

Reverse Mortgage - “ Rising Debt, Falling Equity”

•Social Security benefits are generally not affected
•Interest is deductible when paid
•Reverse mortgage can be:
–A line of credit
–A monthly annuity
–Some combination of above
•Designed for senior homeowners with little or no mortgage debt
•Learning Objectives
LO#4 Explain the characteristics of various mortgage instruments
LO#5 Solve problems related to real estate mortgages
•Next lecture…
•Thank you!
See ya next time!

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QQ： 273427

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