(a). Answer The length of mortgage is 30 years when the monthly payment is $ 1013.37 The length of mortgage is 15 years when the monthly payment is $ 1529.99 Explanation Given: The model: t = 22.264 ln x x − 750 The model approximates the lengths of a home mortgage of $ 200 , 000 at 4.5 % in terms of monthly payment. In the model, t is the length of the mortgage in years and x is the monthly payment in dollars. The monthly payments given: $ 1013.37 $ 1529.99 Calculation: As per the given problem, The model: t = 22.264 ln x x − 750 For the monthly payment of $ 1013.37 x = 1013.37 Substitute the value of x in the model to calculate t t = 22.264 ln 1013.37 1013.37 − 750 = 22.264 ln 3.848 ≈ 30 Therefore, the length of mortgage is 30 years when the monthly payment is $ 1013.37 For the monthly payment of $ 1529.99 x = 1529.99 Substitute the value of x in the model to calculate t t = 22.264 ln 1529.99 1529.99 − 750 = 22.264 ln 1.96155 ≈ 15 Therefore, the length of mortgage is 15 years when the monthly payment is $ 1529.99 (b). To determine To calculate: the approximate amount paid over the term of the mortgage for the given monthly payments. Then calculate the interest amount paid for each payment. Answer For the monthly payment of $ 1013.37 Total amount paid over 30 years is $ 364 , 813.20 The interest amount is $ 164 , 813.20 For the monthly payment of $ 1529.99 The total amount paid over 15 years is $ 275 , 398.20 The interest amount is $ 75 , 398.20 Explanation Given: The model: t = 22.264 ln x x − 750 The model approximates the lengths of a home mortgage of $ 200 , 000 at 4.5 % in terms of monthly payment. In the model, t is the length of the mortgage in years and x is the monthly payment in dollars. The monthly payments given: $ 1013.37 $ 1529.99 The length of mortgage is 30 years when the monthly payment is $ 1013.37 (calculated in part (a)) The length of mortgage is 15 years when the monthly payment is $ 1529.99 (calculated in part (a)) Calculation: As per the given problem, Amount of mortgage = $ 200 , 000 For the monthly payment of $ 1013.37 , the total amount paid over the term of the mortgage, 30 years is = ( $ 1013.37 ) ( 30 ) ( 12 ) = $ 364 , 813.20 The interest amount is $ 364 , 813.20 − $ 200 , 000 = $ 164 , 813.20 For the monthly payment of $ 1529.99 ,the total amount paid over the term of the mortgage, 15 years is = ( $ 1529.99 ) ( 15 ) ( 12 ) = $ 275 , 398.20 The interest amount is $ 275 , 398.20 − $ 200 , 000 = $ 75 , 398.20

8th Edition

ISBN: 9780357022078

Author: Larson

Publisher: CENGAGE L

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Question

Chapter 3.2, Problem 113E

(a).

To determine

To calculate:the approximate lengths of a $200,000 mortgage at 4.5% using the model for the given monthly payments.

(a).

Expert Solution

Answer to Problem 113E

The length of mortgage is 30 years when the monthly payment is $1013.37

The length of mortgage is 15 years when the monthly payment is $1529.99

Explanation of Solution

Given:

The model:

t=22.264lnxx−750

The model approximates the lengths of a home mortgage of $200,000 at 4.5% in terms of monthly payment.

In the model, t is the length of the mortgage in years and x is the monthly payment in dollars.

The monthly payments given:

$1013.37

$1529.99

Calculation:

As per the given problem,

The model:

t=22.264lnxx−750

For the monthly payment of $1013.37

x=1013.37

Substitute the value of x in the model to calculate t

t=22.264ln1013.371013.37−750 =22.264ln3.848 ≈30

Therefore, the length of mortgage is 30 years when the monthly payment is $1013.37

For the monthly payment of $1529.99

x=1529.99

Substitute the value of x in the model to calculate t

t=22.264ln1529.991529.99−750 =22.264ln1.96155 ≈15

Therefore, the length of mortgage is 15 years when the monthly payment is $1529.99

(b).

To determine

To calculate: the approximate amount paid over the term of the mortgage for the given monthly payments.

Then calculate the interest amount paid for each payment.

(b).

Expert Solution

Answer to Problem 113E

For the monthly payment of $1013.37

Total amount paid over 30 years is $364,813.20

The interest amount is $164,813.20

For the monthly payment of $1529.99

The total amount paid over 15 years is $275,398.20

The interest amount is $75,398.20

Explanation of Solution

Given:

The model:

t=22.264lnxx−750

The model approximates the lengths of a home mortgage of $200,000 at 4.5% in terms of monthly payment.

In the model, t is the length of the mortgage in years and x is the monthly payment in dollars.

The monthly payments given:

$1013.37

$1529.99

The length of mortgage is 30 years when the monthly payment is $1013.37 (calculated in part (a))

The length of mortgage is 15 years when the monthly payment is $1529.99 (calculated in part (a))

Calculation:

As per the given problem,

Amount of mortgage =$200,000

For the monthly payment of $1013.37 , the total amount paid over the term of the mortgage, 30 years is

=($1013.37)(30)(12)=$364,813.20

The interest amount is

$364,813.20−$200,000=$164,813.20

For the monthly payment of $1529.99 ,the total amount paid over the term of the mortgage, 15 years is

=($1529.99)(15)(12)=$275,398.20

The interest amount is

$275,398.20−$200,000=$75,398.20

Chapter 3.2, Problem 112E

Chapter 3.2, Problem 114E

Chapter 3 Solutions

EP PRECALC.GRAPHING APPR.-WEBASSIGN-1YR

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the approximate lengths of a $ 200 , 000 mortgage at 4.5 % using the model for the given monthly payments.

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To calculate:the approximate lengths of a $200,000 mortgage at 4.5% using the model for the given monthly payments.

Answer to Problem 113E

Explanation of Solution

To calculate: the approximate amount paid over the term of the mortgage for the given monthly payments. Then calculate the interest amount paid for each payment.

Answer to Problem 113E

Explanation of Solution

Chapter 3 Solutions

To calculate: the approximate amount paid over the term of the mortgage for the given monthly payments.

Then calculate the interest amount paid for each payment.