Formulating Brokerage Success
Don’t just count on automated calculations — understand the math behind mortgages
By Gary Opper, president, Approved Financial Corp.
Nu m b e r s r e pr e s e n t t h e backbone of the mortgage busi- ness. As such, mortgage brokers
need to know their math.
Counting on automated calculations
without understanding what is being calculated can lead to having uninformed
clients and a damaged reputation. Here is
a look at some of the most-important formulas, constants, guidelines and rules of
thumb commonly used in the mortgage
Interest is the lifeblood of mortgages.
Mortgage lenders generally charge interest
monthly, and interest calculations involve
the following variables:
I: ■ Interest amount, or the cost in dollars
for the money borrowed
P: ■ Principal, or the amount of money
R: ■ Interest rate, or the percentage that
must be paid for the use of the money. This
can be expressed as an annual rate, monthly
rate or other periodic rate.
T: ■ Term, or the period for which the
money will be borrowed. The T-factor’s
time expression must correspond to R. For
example, if the interest rate is on an annual basis, then the term must be quoted
The basic formulas for calculating interest are:
I ■ = P*R*T
P ■ = I/(R*T)
R ■ = I/(P*T)
T ■ = I/(P*R)
For example, if the principal loan
amount is $10,000, the annual interest rate
is 6 percent and the term is six months,
then the calculation is as follows:
$10,000*0.06*1/2 ■ = $300.
This calculation is used for simple finance problems.
Complex mortgage calculations — such
as calculating the monthly payment when
given the interest rate, the term and the
principal amount — are best accomplished
with the aid of a calculator or a computer.
Various software programs have built-in features that perform the calculations
concerning mortgages. These calculations
are generally prepared in an amortization
schedule or another printout. These formulas are useful in programming a mortgage spreadsheet.
Below are the formulas for determining various complex mortgage calculations, preceded by abbreviations used in
Pmt: ■ Periodic payment
PV: ■ Present value
FV: ■ Future value
i: ■ Interest rate, or the percentage that must
be paid for the use of the money. This can be
expressed as an annual rate, monthly rate or
other periodic rate and must properly relate
to the number of payments expression.
n: ■ Number of payments (e.g., 360 monthly
payments for a 30-year loan)
The calculation of a periodic payment
of an amount borrowed (present value) is:
Pmt ■ = PV*i/(1-(1/(1+i)n))
This will calculate a monthly payment
given the present value, interest rate and
The calculation of a future value of a
lump sum is:
FV ■ = PV*(1+i)n
The calculation of the present value of a
future sum (balloon payment) is:
PV balloon ■ = FV/(1+i)n
The calculation of the present value of
periodic payments (monthly payments) is:
PV periodic payments ■
Finally, the periodic payments of an
amount borrowed and the present value of a
future sum (balloon payment) can be combined to create the formula for the present
value of a balloon mortgage as follows:
Periodic payments + balloon payment ■
For example, at 8 percent, a sum of
money will double in nine years (72/8).
Some brokers use the following as a rule of
thumb: A 1-point increase in the mortgage
lender’s fee yields a one-eighth-percent decrease in the interest rate of a 30-year loan.
In reality, however, a 1-point fee increase
actually can decrease the interest rate of a
30-year loan anywhere from one-hundredth
of a percent to one-sixth of a percent.
A mortgage lender usually will have its own
underwriting guidelines. One of the guidelines will be the qualifying ratio. There are
many different definitions of two popular
qualifying ratios — the front-end ratio
and the back-end ratio. The commonly accepted definitions are:
Front-end ratio ■ = total housing expenses/
stabilized gross income
Back-end ratio ■ = (total housing expenses
+ total fixed expenses)/stabilized gross
The front-end ratio involves a client’s
total housing expenses. Some lenders include all housing expenses; others include
only the mortgage payment and mortgage insurance. The front-end ratio also
may include real estate taxes, insurance,
maintenance, utilities, and homeowner
or condominium dues. The back-end ratio incorporates all monthly obligations.
The front-end ratio always will be smaller
than or equal to the back-end ratio.
Total fixed expenses include a client’s
total monthly obligations. Obligations that
have fewer than six to 10 months remaining often are not included.
documentary stamp on the note would
cost $353.50. There are 1,010 units of $100
in $101,000, and 1,010 multiplied by $0.35
equals $353.50. If the mortgage note were
$100,901, the stamp tax would be the same
because amounts are rounded to the next
Intangible tax on mortgage: ■ The intangible tax in Florida is 0.2 percent of
the amount of the mortgage. The intangible tax on $101,000 is $202. The calculation for the intangible tax is exact and not
Transfer tax: ■ Most states tax the transfer
of real estate. Different states have different
names for the transfer tax. Transfer tax also
is known as revenue-stamp tax or docu-mentary-stamp tax. In Florida, these taxes
amount to 55 cents per $100. The calculation
is the same as for the documentary stamps
on the note. Amounts are always rounded
up to the next $100 unit.
Gary Opper is president
of Approved Financial
Corp., a licensed mortgage lender in Weston,
Fla. He also does mortgage consulting. He is
a certified public accountant and holds a
certified-financial-planner license. Opper
is a member of the National Association of
Mortgage Brokers, the Florida Association of
Mortgage Brokers and the American Institute
of Certified Public Accountants. Call Opper
at (954) 384-4557, fax (954) 384-5483 or
The rule of 72
Rule of 72 is a quick way to calculate how long
it takes to double a lump sum at a given interest rate. Divide 72 by the given interest rate
to determine the years needed to double the
investment. Conversely, divide 72 by a given
number of years to determine the interest
rate needed to double the investment.
Most states have laws that impose taxes
and fees on the creation of a mortgage and
the transfer of real property. The following
example illustrates how to calculate these
taxes for Florida. The procedure is similar
in most states.
Documentary stamps on note: ■ These
stamps cost 35 cents per $100 or fraction
thereof. On a $101,000 mortgage, then, the
Real estate taxes
Real estate tax rates are expressed as
mills. A mill is one-thousandth of a dollar. Hence, there are 1,000 mills in a dollar.
A mill expressed as a decimal is 0.001. A
home taxed at 21 mills may be expressed
21 mills per $1 of tax-assessed value ■
$0.021 per $1 of tax-assessed value ■
$0.21 per $10 of tax-assessed value ■
$2.10 per $100 of tax-assessed value ■
$21 per $1,000 of tax-assessed value ■
For example, a home with $100,000 of
tax-assessed value after its homestead exemption (which owners in certain states
can take on their primary residence) and
any other exemptions, at a tax rate of 21
mills, would have real estate taxes of $2,100.
The tax assessment is the value that the
municipal government gives real property.
It is not necessarily the fair market value.
There are three methods for determining
an estimate of the fair market value: cost
approach, market approach and income