Example: Loan amortization
Suppose you want to borrow money to buy a house.
You are considering a 15year or a 30year loan.
The lender offers different interest rates, reflecting
the differences in risks of shorterterm and longerterm
lending. For the 15year loan, the annual rate
is 6.25% (compounded monthly, with 180 equal monthly
payments). For the 30year loan, the annual rate
is 6.75% (compounded monthly, with 360 monthly
payments). If you borrow $150,000, what would
your monthly payments be for each loan?
Answer:
What is the stream of payments necessary to
pay off an increasing sum? Use the present value
formula to calculate the present value of Pymt_{n}
deposited at the end of n periods discounted
at i percent:
PV = Pymt_{n} * [(1+i)^{n}
 1] / (1+i)^{n} * i
Solve for Pymt_{n} for the
15year loan:
PV = Pymt_{n} * [(1+i)^{n}
 1] / (1+i)^{n} * i
Pymt_{180} = $150,000
/ [(1+.0625/12)^{180}  1] / [(1 + .0625/12)^{180}
* .0625/12]
Pymt_{180} = $1,286.13
Aren't spreadsheets and calculators
grand! Tables would work, but they would have
to be big. The monthly payments for the 30year
loan would be $972.90. Click here to view a loan
amortization spreadsheet. Many similar programs
are also imbedded in realtors' websites  see
Dan River Realty's (Pilot Mountain, NC) calculator.
Which loan is better? That depends
on what you would do with the difference between
$1,286.13 and $972.90 for the first 15 years.
Would it be worth having that extra $313.23 for
fifteen years and then paying $972.90 for another
fifteen years? Your call  depending perhaps
on your personal preference for immediate gratification.
Should you pay off your mortgage? Some
homeowners are wondering whether savings in CDs
and money market accounts might be better used
to reduce or eliminate mortgage payments. There
are downsides to paying down, or paying off, your
mortgage.
Debating the Pros and Cons Of Paying Off Your
Mortgage, Fiscally Fit / Terry Cullen, Wall
Street Journal Online  April 10 03.
