APPLICATIONS OF EXPONENTIAL AND
LOGARITHMIC FUNCTIONS

(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:

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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 3: Suppose a bank offers you a 9% interest rate on a 25-year mortgage to be paid back with monthly payments. Suppose the most you can afford to pay in monthly payments is $700. How much of a mortgage could you afford?

Answer: $83,413.14

Solution and Explanations:

Step 1: In the equation

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substitute 9% for r (the annual interest rate), 12 for n (the number of payments per year, 25 for t (the number of years), and $700 for P (the mortgage payment). You are solving for M (the amount of the mortgage you can afford)

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Step 2: Multiply both sides of the above equation by 12:

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Step 3: Simplify the right side of the above equation:

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Step 4: Multiply both sides of the above equation by 0.0893712166187:

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Step 5: Divide both sides of the above equatio by .09:

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If you would like to review another example, click on Example.

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Author: Nancy Marcus

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