(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:
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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