The model t = 16.625 ln(x/x - 750), x > 750 approximates the length of a home mo

Question

The model t = 16.625 ln(x/x - 750), x > 750 approximates the length of a home mortgage of $150,000 at 6% in terms of the monthly payment. In the model, t is the length of the mortgage (in years) and x is the monthly payment (in dollars). a) Use the model to approximate the lengths of a $150,000 mortgage at 6% when the monthly payment is $897.72. b) Approximate the total amounts paid over the term of the mortgage with a monthly payment of $897.72. c) Approximate the total interest charges for a monthly payment of $897.72. d) What is the vertical asymptote for the model? Interpret its meaning in the context of the problem.

Explanation / Answer

a) t = 16.625 ln ( x / x - 750 )

plugging x = 897.72

t = 16.625 ln ( 897.72 / 897.72 - 750 )

t = 30 years

length of mortgage is 30 years

b) amounts paid by him over the term is 30*12*897.72

= $ 323179.2

c) total interest = 323179.2 - 150,000

= $ 173179.2

d) vertical asymptote is 750

this means that minimum monthly payment cannot be less than $ 750

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