Assignment 1 solutions_Winter 2010

Assignment 1 solutions_Winter 2010 - AP/ADMS4504 Assignment...

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AP/ADMS4504 Assignment #1 Solutions Winter 2010 Question 1 (10 marks) This question has two related parts, (a) and (b). Please note : in both parts (a) and (b) below, first assume the mortgage is a Canadian mortgage, and then redo the calculations assuming an American mortgage. Consider the following Adjustable Rate Mortgage (ARM): Jennifer bought a house three years ago (January 1, 2007) at a price of $400,000. The interest rate for the first three years of this 30-year mortgage was fixed at 3% APR semiannually compounded and no down payment was required. Starting Year 4, (January 1, 2010) the rate adjusts to the Treasury rate plus 3.6% (also APR, compounded semiannually). (a) If the Treasury rate now (January 1, 2010) stands at 4%, what will be the difference in monthly payments between Jennifer’s December 1, 2009 and January 1, 2010 payments? (6 marks) Answer 1) We first assume this is a Canadian mortgage . Find the original monthly mortgage payment: An APR of 3% with semiannual compounding is equivalent to a monthly mortgage rate i m as given by: %. 2485 . 0 i % 0225 . 3 1 ) 2 / % 3 1 ( 1 ) i 1 ( EAR m 2 12 m = = + = + = The mortgage originally has a life of 30 years or 360 months. Its original monthly mortgage payment is: . 54 . 682 , 1 $ PMT ] %) 2485 . 0 1 %( 2485 . 0 1 % 2485 . 0 1 [ PMT ] ) r 1 ( r 1 r 1 [ PMT 000 , 400 $ 360 n = + × = + × = Now find the new monthly mortgage payment starting January 1, 2010: The remaining principal of the mortgage after 3 years (with 27 years or 324 months remaining) is: $1,682.54 × PVAF (0.2485%, 324) = $374,104.80, where PVAF stands for present value annuity factor.
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AP/ADMS4504 Winter 2010 Assignment #1 Solutions The new (and much higher) mortgage rate is 7.6% (= 4% + 3.6%) semiannually compounded. It follows that the new monthly mortgage rate is: %. 6235 . 0 i % 7444 . 7 1 ) 2 / % 6 . 7 1 ( 1 ) i 1 ( EAR m 2 12 m = = + = + = So the new monthly mortgage payment is found by: $374,104.80 = PMT × PVAF (0.6235%, 324) PMT = $2,691.83. It follows that the difference in monthly mortgage payments is $(2,691.83 - 1,682.54) = $1,009.29 between December 1, 2009 and January 1, 2010. 2) Now let’s assume this is an American mortgage instead. Find the original monthly mortgage payment: An annual mortgage rate of 3% is equivalent to a monthly rate i m of 0.25%. The original monthly mortgage payment is: . 42 . 686 , 1 $ PMT ] %) 25 . 0 1 %( 25 . 0 1 % 25 . 0 1 [ PMT ] ) r 1 ( r 1 r 1 [ PMT 000 , 400 $ 360 n = + × = + × = Next find the new monthly mortgage payment starting January 1, 2010: The remaining principal of the mortgage after 3 years is: $1,686.42 × PVAF (0.25%, 324) = $374,177.50. Given the new mortgage rate of 7.6%, the new monthly mortgage rate is
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Assignment 1 solutions_Winter 2010 - AP/ADMS4504 Assignment...

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