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CH 10] Calculating Business 10-11

Calculating the periodic payment for a Fully Amortized loan.
The loan payment equation is used to calculate the payments on a loan. The equation
used to calculate loan payments is the same as the equation used to calculate
payments on an ordinary annuity which has been discussed. A loan, by definition, is an
annuity, in that it consists of a series of future periodic payments.

Pmt = Monthly Payment 10
PV = Present Value, Loan Amount
r = Interest rate per month (Annual interest rate ÷ payments per year. i.e. 5%/yr =
0.05 ÷ 12 months)
n = number of payment periods
r
Pmt = PV - n
1 — (1 + r)

The PV, or present value, portion of the loan payment equation uses the original loan
amount. The original loan amount is essentially the present value of the future payments
on the loan, much like the present value of an annuity.
It is important to keep the rate per period and number of periods consistent with one
another in the equation. If the loan payments are made monthly, then the rate per period
needs to be adjusted to the monthly rate and the number of periods would be the number
of months on the loan. If payments are quarterly, the terms of the loan payment equation
would be adjusted accordingly to reflect quarterly (every 3 months) payments.

Standard Loan Payment
The loan payment equation shown is used for a standard fully amortized loan which
has a set loan life and fixed interest rate. There are other common loans in use that do not
hold specifically to the payment equation illustrated which include a graduated payment,
negatively amortized, interest only, option, balloon payment loans, and adjustable rate or
variable rate loans.
An Adjustable Rate Mortgage loan is used by lenders who will offer an exceptionally
low interest rate to potential customers who would not ordinarily qualify for a standard
loan. The annual interest rate and monthly payment is generally below the current market
so that their budget qualifies for the payment they will make. There is a danger to this
type of loan in that the financial agreement signed allows the lender to change the rate,
which is generally up, and when the loan rate (interest rate on the loan) does change, the
payments can be so high that they no longer fit within the borrower’s budget and may
force a quick sale. The loan payment equation is used again and a recalculation is made
based on the revised interest rate. If a sale is initiated it is hoped that equity has been
gained in the property to return a profit, however modest it may be, to yield a return to
the seller.

Use of Loan Payment Equation
The loan payment equation can be used to calculate any type of conventional loan
including mortgage, consumer, and business loans. The equation does not differ based on
what the money is spent on, but only when the terms of repayment deviate from a
standard fixed amortization.
This equation is especially valuable for planning and budgeting to determine what
payment structure best fits your finances. Note that a fully amortized loan will pay down
both interest owed and principal with a level payment each month; a payment amount
that does not change. Having a level pre-determined payment structure that the amortized
loan offers allows the budgeter to know what their budget charges will be and thus is able
to make better financial choices for their money.
Remember that in the payment structure interest is paid first and then the balance of
the payment reduces the loan amount.
Increasing the level payment does reduce the overall interest that would accrue on a
loan with the result of shortening the life of the loan. Paying more on each payment does
effect the overall budgeting process and the amount of dollars available for other
purchases.

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