B). Over the past 40 years, interest rates have varied widely. The rate for a 30

Question

B). 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.)

Explanation / Answer

The formula for computing the fixed monthly payment for amortizing a loan of $ L over a term of n months at a monthly interest rate of r is

P = L [r(1 + r)n]/[(1 + r)n - 1] so that L = (P/r) [(1 + r)n - 1]/ [(1 + r)n ]. Here, P = $ 893.33, r = 4.64/1200 = 29/7500 and n = 30*12 = 360. Then L =

[893.33/(29/7500)][(1+29/7500)360 -1]/[ (1+29/7500)360 ] = 231033.62*(3.012103705)/(4.012103705) = $ 173449.46 ( on rounding off to the nearest cent).

Thus, if we can afford to pay a monthly amount of $893.33, we can borrow $ 173449.46 if the term is 30 years and the interest rate is 4.64%.

Note:

This part of the question does not mention property tax, hence it has not been accounted for.

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