SOLUTION: Over the past 40 years, interest rates have varied widely. The rate for a 30-year mortgage reached a high of 14.75% in July 1984, and it reached 4.64% in October 2010. A significan

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Question 1118848: Over the past 40 years, interest rates have varied widely. The rate for a 30-year mortgage reached a high of 14.75% in July 1984, and it reached 4.64% in October 2010. A significant impact of lower interest rates on society is that they enable more people to afford the purchase of a home. In the following exercise, we consider the purchase of a home that sells for $125,000. Assume that we can make a down payment of $25,000, so we need to borrow $100,000. We assume that our annual income is $43,000 and that we have no other debt. Assume that property taxes plus insurance total $250 per month.
If we can afford to pay a monthly amount of $753.33, what is the difference in the amount we can borrow between the high and low rates mentioned above? (Round your answer to the nearest dollar.)
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the high rate is 14.75% per year.
the low rate is 4.64% per year.

the mortgage amount is 100,000
the length of the mortgage is 30 years.

assuming the $753.33 is the amount that we can use to pay off the mortgage, then the following applies, when using the following calculator.

https://arachnoid.com/finance/

a payment of $753.33 at the end of each month for 30 years at 14.75% interest rate per year will be able to service a mortgage of 60,533.91.

here's a picture of the calculations.
the inputs are everything except the present value.
the output is the present value.
the interest rate is 14.75% / 12 = 1.229167% per month.
the number of time periods is 30 * 12 = 360 months.

$$$

a payment of $753.33 at the end of each month for 30 years at 4.64% interest rate per year will be able to service a mortgage of $146,266.98.

here's a picture of the calculations.
the inputs are everything except the present value.
the output is the present value.
the interest rate is 4.64% / 12 = .386667% per month.
the number of time periods is 30 * 12 = 360 months.

$$$

at 14.75% per year, we could not afford to pay the mortgage.

at 4.64% per year, we could easily afford to pay the mortgage.

the maximum interest rate per year that would allow us to pay off the $100,000 mortgage with payments of $753.33 at the end of each month, would be .689945% per month * 12 = 8.27934% per year.

here's a picture of the calculations.
the inputs are everything except the interest rate percent.
the output is the interest rate percent per month.
the interest rate per month is multiplied by 12 to get the interest rate per year.
the number of time periods is 30 * 12 = 360 months.

$$$


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Over the past 40 years, interest rates have varied widely. The rate for a 30-year mortgage reached a high of 14.75% in July 1984, and it reached 4.64% in October 2010. A significant impact of lower interest rates on society is that they enable more people to afford the purchase of a home. In the following exercise, we consider the purchase of a home that sells for $125,000. Assume that we can make a down payment of $25,000, so we need to borrow $100,000. We assume that our annual income is $43,000 and that we have no other debt. Assume that property taxes plus insurance total $250 per month.
If we can afford to pay a monthly amount of $753.33, what is the difference in the amount we can borrow between the high and low rates mentioned above? (Round your answer to the nearest dollar.)
With a monthly affordable amount of $753.33, and with $250 deducted for property taxes and insurance, the amount remaining to pay the mortgage is $503.33 ($753.33 - 250)

With a  monthly mortgage payment of $503.33, over a 30-year period, and an annual interest rate of 14.75%, the amount that one can borrow is $40,445.

With a  monthly mortgage payment of $503.33, over a 30-year period, and an annual interest rate of 4.64%, the amount that one can borrow is $97,727.

The difference between these 2 mortgage loans is: $97,727 - 40,445 = highlight_green%28%22%2457%2C282%22%29%29