# 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 1: Find the monthly payments on a \$100,000, 30-year mortgage, with monthly payments at 9.5%. How much interest will you pay over the 30 years?

Answer: The monthly payments are \$840.85. You will pay a total of \$302,706 over the 30-year mortgage; \$202,706 os this amount will be interest.

Solution and Explanations:

Step 1: In the equation

substitute \$100,000 for M (the mortgage amount), 12 for n (the number of payments per year, 30 for t (the number of years), and 9.5% for r (the annual interest rate)). You are solving for P (the monthly payment)

The mortgage payment is \$840.85 per month.

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