(Amortization Word Problems)
To solve an exponential or logarithmic word problem, convert the
narrative to an equation and solve the equation.
There is a relationship between the mortgage amount, the number
of payments, the amount of the payment, how often the payment
is made, and the interest rate. The following formulas illustrate
the relationship:
where P = the payment, r = the annual rate, M = the mortgage
amount, t = the number of years, and n = the number of payments
per year.
Example 2: Suppose you wanted to take out a mortgage for
$75,000 with monthly payments at 7%, but you could only afford $450
per month payments. How long would you have to make payments to pay
off the mortgage, and how much interest would you pay for this payment
period?
Answer: It would take you 616.10755485 months to pay off the
mortgage, roughly 51 years and 5 months. The bank would either have
you pay 616 payments of $450 per month and one last payment of
$48.40 or your 616th payment would be $498.40.
Solution and Explanations:
substitute $75,000 for M (the mortgage amount), 7% for r (the annual interest rate), 12 for n (the number of payments per year, and $450 for P (the mortgage payment). You are solving for t (the number of months that you must make payments)
to get:
If you would like to review another example, click on Example.
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Author: Nancy Marcus