Question

10. The monthly mortgage payment in dollars, P, for a house is a function of three variables: P f(A, r, N), where A is the amount borrowed in dollars, r is the in- terest rate, and N is the number of years before the mort gage is paid off (a) f(92000, 14, 30) 1090.08. What does this tell you, in financial terms? 72.82. What is the financial (92000,14,30) significance of the number 72.82? tive? Why? tive? Why? (c) Would you expect ???? to be positive or nega- (d) Would you expect 0P/ON to be positive or nega-

Answer 1

10. Monthly Payments is given by

= Loan*(Interest/12)/(1-(1+Interest/12)^-(12*Time))

a. f(92000,14,30) = 1090.08 means he has to pay 1090.80 monthly for his mortgage for next 30 years.

b. 72.82 means monthly payment has a direct correlation with the interest rate and for 92000 and 30-year mortgage it has a slope of 72.82

c. For differential of payment with respect to the amount borrowed "(Interest/12)/(1-(1+Interest/12)^-(12*Time))", it would act as a constant and A being positive, the differential would also be positive

d. For differential of payment with respect to the time "Loan*(Interest/12)", it would act as a constant and

(1-(1+Interest/12)^-(12*Time))^-1 would be differentiated.

After differential it would become: -1*(1-(1+Interest/12)^-(12*Time))^-2 * -(Ln(1+Interest/12)*(-12)*(1+Interest/12)^-(12*Time))

So Sign would be negative

24. Dear student as per HOMEWORKLIB POLICY only one question per post is allowed and ideally, it belongs to advanced mathematics, but as per my knowledge following should be the answers:

a. negative

b. positive

c. negative