Question

A family in Melbourne purchased a house in October 2019. A local bank approved a loan of L = $500,000 at a fixed annual interest rate ofr = 3.25% for this family to settle the purchase. The loan need to be paid over 25 years through monthly repayments of an equal amount m (in dollars). Note that m depends on r and is treated as a function of r denoted as m(r). (1) Calculate the monthly repayment amount m(r) when r = 3.25%. (2) Use the following first-order approximation to approximate the monthly repayment if the interest rate is reduced by 0.25% (that means the interest rate becomes 3%). m(r) = m(ro) + m' (ro) x (r - ro), wherer = 3% and ro = 3.25%.

Answer 1

#500000 XD-00271 4(1.00271)300 11.0027183001 4 500000X0-00271 x 2252 2.252-1 으 -$500000 X0-00271X1999 y $2437.47 E.M.I if r= 3:25% is $237.47) I E.M.I ifo = 3% pale 0.2518m. EMT=8500000 0.0025 x 11-00257700 (1.0025) 500, 4 $500oooX0.00258 2:12 VividA 2-12-1 =$5000ooX 0.0025x 1.89 4 = $2360.52 so E.M.I if s= 37.8.9 = $2360.52