Question

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.

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.)

Answer 1

Given, remaining amount after down payment = $100000

High interest rate = 14.75%

Low interest rate = 4.64%

Now, the amount to be borrowed monthly with high interest rate = ${100000+[100000*14.75/(12*100)]}

And, the amount to be borrowed monthly with low interest rate = ${100000+[100000*4.64/(12*100)]}

Therefore, the difference in the amount that can borrow between the high and low rates is =

${100000+[100000*14.75/(12*100)] - 100000-[100000*4.64/(12*100)]}

= $[100000*{(14.75-4.64)/1200}]

= $[100000*10.11/1200]

= $842.5

$842

Hence, the required difference is $842.