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 $49,000 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 $893.33, determine how much we can borrow if the term is 30 years and the interest rate is 4.64%. (Round your answer to the nearest dollar.)
$   ???

Answer 1

Let, within x months, they will be repaid the whole amount.

Then, after x months, the whole amount will be = ${100000+[(100000*x*4.64)/(100*12)]}

And, after x months, the repaid amount will be = $[893.33*x] = $[2680*x/3]

By condition, 100000+[(100000*x*4.64)/(100*12)] = 2680*x/3

i.e., 100000*[1+{x*4.64)/(100*12)}] = 2680*x/3

i.e., 1000*[1200+(x*4.64)]/12 = 2680*x/3

i.e., 100*[1200+(x*4.64)] = 1072*x

i.e., 120000+(464*x) = 1072*x

i.e., (1072*x)-(464*x) = 120000

i.e., 608*x = 120000

i.e., x = 120000/608

Therefore, the repaid amount will be = ${100000*[1+{(120000/608)*4.64/1200}]} $176316.