Question

Prime Mortgage Company sanctions a loan application for a 30 year mortgage loan for
US$100,000. The interest rate on the loan is 12% per annum and the borrower is required to
make equated monthly payments to repay the loan in 30 years (360 months). If the market
rate of interest goes down to 9% per annum, is the loan still worth US$100,000? Why? Why
not? (5 points)

b) If the corn farmer in the example above harvests 60,000 bushels, what amount will he
receive? What if he had not hedged his position? If the corn farmer in the example is able to
harvest only 40,000 bushels and the price per bushel rises to US$3.90 due to short supply of
corn, will his exposure be completely hedged? Why? Why not? Support your answer with
calculations. (5 points)

Answer 1

(1) Mortgage Tenure = 30 years or (30 x 12) = 360 months, Mortgage = $ 100000, Interest Rate = 12 % per annum

Applicable Monthly Rate = 12 / 12 = 1 %

Let the monthly repayments be $ p

Therefore, 100000 = p x (1/0.01) x [1-{1/(1.01)^(360)}]

100000 = p x 97.218331

p = 100000 / 97.218331 = $ 1028.6126 ~ $ 1028.61

If the Interest Rate goes down to 9 %, then Applicable Interest Rate per Month = 9/12 = 0.75 %

If the monthly mortgage repayments stay constant at $ 1028.61 then mortgage value = 1028.61 x (1/0.0075) x [1-{1/(1.0075)^(360)}] = $ 127837.89

As is observable, for a fixed monthly repayment the interest rate and mortgage values are inversely related. Hence, if the interest rate goes down the value of the mortgage will go up and vice-versa.

NOTE: Please raise a separate query for the solution to the second unrelated question as one query is restricted to the solution of only one complete question with up to four sub-parts.