Question

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

Answer 1

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