Question

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Lab 2 - Differentials and your Mortgage – FA19 The monthly payment P on a mortgage loan of A dollars at an APR of r (as a decimal) for t years is given by this formula. P(A,r,1)= A - -12 1. Determine and state the partial derivatives using a CAS (Computer Algebra System.) Include screen shots of each of these in your report! (15 pts) 2. Find P(275000, 0.04, 20). (10 pts) 3. Use differentials to determine the change in the payment amount (found in #2) if the loan amount increases by 10%, or the APR increases by 10% to 4.4%, or the number of years increases by 10%. Do each change separately. (30 pts) 4. Use differentials to determine the change in the payment amount (found in #2) if the loan amount increases by one dollar, or the APR increase by 1% to 5%, or the number of years increases by 1. Do each change separately. (30 pts) 5. Find the exact change in the payment amount for each of the three cases in #3.(15 pts) (Hint: In problems #3 and #4 you are calculating dP. In #6 you are calculating AP.)

Answer 1

P (Art) = A. / - (142) - 12 72 1- (1+ 2+ -12- n 0-(***) *** *** [1-(1+) ] . A L -(+7) * * [-(*) ] - at - A. (- 12) dan (17 / 8 ) . (1+2 -12 + [-(+)R] .-A. (1+1). (1 ) [ - (14 4 Joker 2 P ( 275000, 0. 04, 20) = 275000. 2/12 -lit 0.041-240 - 1666.45 (Approx) From a dp = DA. 12 - 10 -. A. 100 T-(17 %1.12t - loo - (+-+2) Payment P will increase [ 2A = 10% ] by 10% i.e. P'a tett 1866.45 + 10% (1964 = 1933.095