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 1: What is the monthly payment on a mortgage of $75,000
with an 8% interest rate that runs for 20 years, 25 years, 30
years? How much interest is paid over 20 years, 25 years, 30
years?
Answer: 20 years: payment = $627.33 per month; after 20 years
of payments, you will have paid $150,559.20 ($75,559.20 in
interest)
25 years: payment = $578.86 per month; after 25 years of payments,
you will have paid $173,658.00 ($98,658.00 in interest).
30 years payment = $$550.32 per month; after 30 years of payments,
you will have paid $198,116.43 ($123,116.43 in interest).
Solution and Explanations:
substitute $75,000 for M (the mortgage amount), 8% for r (the annual interest rate), 20 for t (the number of years), and 12 for n (the number of payments per year. You are solving for P (the monthly payment for the 20 years)
The monthly payment will be $627.33. After 20 years of payments, you will have paid
Everything over the initial $75,000 is interest. Therefore, after 20 years, you will have paid
in interest.
substitute $75,000 for M (the mortgage amount), 8% for r (the annual interest rate), 25 for t (the number of years), and 12 for n (the number of payments per year. You are solving for P (the monthly payment for the 25 years)
The monthly payment will be $578.86. After 25 years of payments, you will have paid
Everything over the initial $75,000 is interest. Therefore, after 25 years, you will have paid
in interest.
substitute $75,000 for M (the mortgage amount), 8% for r (the annual interest rate), 30 for t (the number of years), and 12 for n (the number of payments per year. You are solving for P (the monthly payment for the 30 years)
The monthly payment will be $550.32. After 30 years of payments, you will have paid
Everything over the initial $75,000 is interest. Everything over the initial $75,000 is interest. Therefore, after 30 years, you will have paid
in interest.
If you would like to review another example,
click on Example.
Work the following problems. If you want to check your answer
and solution click on Answer.
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Author: Nancy Marcus