The term t (in years) of a $200,000 home mortgage at 7.5% interest can be approximated...

The term t (in years) of a $200,000 home mortgage at 7.5% interest can be approximated by the function below, where x is the monthly payment in dollars.

t = 13.375 ln( x/ x-1250) , x > 1250

(a) Use a graphing utility to graph the model.,

(b) Use the model to approximate the term of a home mortgage for which the monthly payment is $1390. (Round your answer to the nearest year.)
________ yr

What is the total amount paid? (Round your answer to two decimal places.)
$

(c) Use the model to approximate the term of a home mortgage for which the monthly payment is $1610. (Round your answer to the nearest year.)
yr

What is the total amount paid? (Round your answer to two decimal places.)
$

(d) Find the instantaneous rates of change of t with respect to x when x = $1390 and x = $1610. (Round your answers to four decimal places.)

t '(1390) =
t '(1610) =

(e) What are the benefits (if any) of higher monthly payment. (Select all that apply.)

a. there are no benefits

b. payment over a shorter term

c. a lower total amount paid

d. the two payments are the same

Solutions

Expert Solution

(e) For higher monthly payment, both duration of payment is short and less sum is payed. Hence option B and C are correct.

milcah answered 1 year ago

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