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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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<h3>Answer: D) 1692 miles</h3>
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Explanation:
A diagram is very handy for this type of problem. Refer to the diagram below (attached image). Here are the steps used to form the diagram
- Plot point A and make that the home base. Plot point D directly south of point A. I'm skipping B and C because those will be used to form the triangle later.
- Imagine you are standing at point A and looking south at point D. Turn 46 degrees toward the east direction (this is what the notation "bearing of S 46° E" means). Then move 550 miles from A to land on point B. This is the location where the plane makes its first turn.
- Plot the points E and F, which are north and south of point B.
- Imagine we are at point B and looking directly south at point F. Turn 55 degrees toward the west, which is due to the "S 55° W" and then move 483 miles to arrive at point C. This is the plane's location where it turns around to go back to home base.
The diagram below shows all of this visually summarized. We have the segments
- AB = 550 miles
- BC = 483 miles
- AC = x miles
And we have these angles
- Angle DAB = 46 degrees and Angle ABE = 46 degrees (blue)
- Angle ABC = 79 degrees (red)
- Angle ACB = 55 degrees and Angle FBC = 55 degrees (green)
Angle ABC comes from the fact that the blue and green angles add with the red angle to get 180. So we basically need to solve 46+y+55 = 180 which leads to y = 79.
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Once the diagram is set up, we'll use the law of cosines to find x.
Focus on triangle ABC. Ignore points D,E,F. Ignore any extra lines as well.
The interior angles of triangle ABC are
- A = 46 degrees
- B = 79 degrees
- C = 55 degrees
The sides opposite the angles are
- a = 483 (opposite angle A)
- b = x (opposite angle B)
- c = 550 (opposite angle C)
Now we can apply the law of cosines
b^2 = a^2 + c^2 - 2*a*c*cos(B)
x^2 = 483^2 + 550^2 - 2*483*550*cos(79)
x^2 = 434412.180756441
x = sqrt(434412.180756441)
x = 659.099522649229
x = 659
Side AC, or CA, is roughly 659 miles long.
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To find the total distance the plane travels, we add up the three sides of the triangle (ie we find the perimeter)
Distance Traveled = AB + BC + CA
Distance Traveled = 550 + 483 + 659
Distance Traveled = 1692 miles