Suppose a family intends to buy a house and prequalifies at

Suppose a family intends to buy a house and prequalifies at a five year mortgage rate of 2.83% per year. A new government policy 1 about to take effect requires qualification at the contractual five year rate plus 2% (so in this case, a rate of 4.83% per year). Using differentials, estimate dP/P, the relative change in the house price that the family can afford if they wait until after the new policy takes effect. Assume the mortgage principal Pand the monthly payment R are related by a formula of the form

P=R 1?(1+r)^?n/r

where r = 0.0283/12 is the interest rate per month and n = 25 · 12 = 300

is the number of months. Assume the monthly payment R is constant.

Solution

Answer )

Although the formula given in question is not clear , as P=R 1?(1+r)^?n/r Which should be probabily like given below:

Let the family has capacity to pay $ 1 as monthly EMI towards mortgage.

With r= 0.0283/12 , value of P= 1 *( 1- (1+0.0283/12)^(-360))/(0.0283/12) = $242.43

Now witth change of interes rate to r=0.0483/12 value of P= 1 *( 1- (1+0.0483/12)^(-360))/(0.0483/12) = $189.941

change in Principle (dP) =$189.941 -$ 242.43 = -$52.49

dP/P = -$52.49 / $242.43 = 0.2165 = - 21.65%