Monthly Payment 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). Approximate the lengths of a $ 150 , 000 mortgage at 6 % when the monthly payment is $ 897.72 and when the monthly payment is $ 1659.24 . (b). Approximate the total amounts paid over the term of the mortgage with a monthly payment of $ 897.72 and with a monthly payment of $ 1659.24 . What amount of the total is interest costs in each case? (c). What is the vertical asymptote for the model? Interpret its meaning in the context of the problem.
Monthly Payment 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). Approximate the lengths of a $ 150 , 000 mortgage at 6 % when the monthly payment is $ 897.72 and when the monthly payment is $ 1659.24 . (b). Approximate the total amounts paid over the term of the mortgage with a monthly payment of $ 897.72 and with a monthly payment of $ 1659.24 . What amount of the total is interest costs in each case? (c). What is the vertical asymptote for the model? Interpret its meaning in the context of the problem.
Solution Summary: The author explains how to calculate the approximate length of a 150,000- mortgage at
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). Approximate the lengths of a
$
150
,
000
mortgage at
6
%
when the monthly payment is
$
897.72
and when the monthly payment is
$
1659.24
.
(b). Approximate the total amounts paid over the term of the mortgage with a monthly
payment of
$
897.72
and with a monthly payment of
$
1659.24
. What amount of the total
is interest costs in each case?
(c). What is the vertical asymptote for the model? Interpret its meaning in the context of the
You deposit 120 dollars into an account that pays an interest rate of 6% per year.
a.) Find an equation for the amount you have after t years. A(t)=
b.) Use the equation in part (a) to find the doubling time for the amount in your account. Round to two decimal places.
How many years
An investment of $75,000 increases at a rate of 12.5% per year. Find
the value of the investment after 30 yr.
Keyanna invests $900 in a mutual fund that averages 2% growth per year. The amount of money in the fund
is given by A = 900(1.02), where x is time in years.
(a) How long will take for Keyanna's money to double? Round to the nearest tenth of a year.
(b) How long will take for the same investment to triple in value? Round to the nearest tenth of a year.
years
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Check Answer
years
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