Amortization

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Amortization
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A loan with a fixed rate is said to be amortized
when both principal and interest are paid by
a sequence of equal payments made over equal
time intervals.
The idea is that the loan is paid off, or
"killed, at the end of the term of the loan.
(The Latin as well as French word Mort means
death!)
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• As we change our focus from annuities to
  amortization, note the following
• what was a payment to an annuity is now regarded
  as a loan payment.
• the initial value of the annuity was 0 but now
  it is the future value of the loan that is 0.
• the present value of the annuity is the amount
  of the loan received.

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The fundamental question is How much should the
monthly loan payment be so that a loan is
amortized at the end of its the term?
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Example
A person purchased a condo for 260,000. The
condo was financed by making a 10 down payment
and signing a 30-year mortgage at 6.5 on the
unpaid balance.
a) What will be the monthly payments? b)
What will be the total interest paid?
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What difference would a shorter term mortgage
make?
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Example
Compare the monthly payments and the total
amounts of interest paid if a 15-year mortgage is
chosen instead of the 30-year mortgage in the
previous example.
Why do people take long term loans?
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We often want to know the outstanding balance of
a loan. In the case of a mortgage, this is
important to determine the equity that the
homeowner has on the property.
9
Example
John bought a townhouse on September 31, 1995 by
taking out a 30-year, 112,475 mortgage at 9.
a) Calculate the unpaid balance of the loan on
September 31, 2005, just after making the 120th
payment. b) How much equity did John have on
his home if it was appraised at 300,000 on
September 31,2005? c) How much interest was paid
during the first 10 years of the loan? d) How
much interest will be paid during the last 10
years of the loan?
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The last example clearly illustrates that 1)
initially the larger portion of the payments goes
toward payment of interest charges, but 2) as
time passes the larger portion of the payments
goes toward payment of the principal.