# 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:

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.

Problem 3: Suppose a bank offers you a 10% interest rate on a 20-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?

Solution and Explanations:

Step 1: In the equation

10% for r (the annual interest rate), 20 for t (the term of the mortgage in years), 12 for n (the number of payments per year, and \$700 for P (the monthly payment), You are solving for M (the mortgage amount)

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

Step 3: Divide both sides of the equation by (.10):

Step 4: Multiply both sides of the equation by

or 0.863538488989:

The most you afford for a mortgage, given your constraints, is \$72,537.23.

If you would like to work another problem and review the answer and the solution, click on problem.

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