(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
Problem 2: Suppose you wanted to take out a mortgage for
$100,000 with monthly payments at 9%, but you could only afford
$800 per month payments. How long would you have to make payments to
pay off the mortgage, and how much interest would you pay for this
Answer: 371.063 months or 30.92192 years or 30 years and 11
months. You would have 370 payments of $800 and the last payment
would be $850.40. The interest paid over the term of the mortgage
would be $216,850.40.
Solution and Explanations:
substitute $100,000 for M (the mortgage amount), 12 for n (the number of payments per year, $800 for P (the monthly payment), and 9% for r (the annual interest rate)). You are solving for t (the term of the mortgage in years) or 12t( the term of the mortgage in months)
or 371.063064259 or 371 months.
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