|x-7|+5 is greater than or equal to 3

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$\large\begin{array}{l} \textsf{Solve the absolute value inequality:}\\\\ \mathsf{|x-7|+5\ge 3}\\\\ \mathsf{|x-7|\ge 3-5}\\\\ \mathsf{|x-7|\ge -2}\\\\\\ \textsf{Since absolute values always give a non-negative number,}\\\textsf{every real value for x satisfies the inequatily:}\\\\ \textsf{For all }\mathsf{x\in\mathbb{R},}\\\\ \mathsf{|x-7|\ge 0>-2}\\\\\\ \therefore~~\mathsf{|x-7|\ge 2}\\\\ \textsf{regardless of the value of x.} \end{array}$

$\large\begin{array}{l} \textsf{Solution set: }\mathsf{S=\mathbb{R}.} \end{array}$

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Using a spreadsheet program, create an amortization schedule for a 30-year mortgage of $500,000 at an annual interest rate of 4.

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This exercise requires the ability to create Amortization Schedules Using a Spreadsheet program. Based on the information given about the Amortization of the loan, the principal payable per month became greater than the interest payable per month on the 159th month (given that the loan amount is $500,000.

<h3>In which month does the amount of principal in a monthly payment first exceed the amount of interest?</h3>

The amount of principal in a monthly payment first exceeds the interest payment In 159th Month. The interest on this month is $1, 248.39 while the principal on this month is $1, 205.46.

It is to be noted that when a loan is taken, the constituents of the amounts being paid back is the Principal and part of the interest on the loan.

<h3>How do you Calculate Amortization of Loans?</h3>

The yearly interest rate must be divided by 12.

Your monthly interest rate, for instance, will be 0.3525 percent if your annual interest rate is 4.23 percent (0.0423 annual interest rate x 12 months).

Additionally, you'll add 12 to the number of years remaining on your loan term.

<h3>How much interest is repaid for the term of the loan?</h3>

The total amount of interest that is paid for the term loan is $383,385.54

<h3>If the loan amount was $750,000 instead of $500,000, would the month in which the amount of principal in a monthly payment first exceeded the amount of interest change?</h3>

Yes it would change. It would change to the 165th month. In this month, the interest paid is $1, 834.00 while the principal paid back is $1,846.77. See the attached image for answer C.

Learn more about Amortization at;
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