You have been paying $800 as monthly installments for the mortgage of your new h

Question

You have been paying $800 as monthly installments for the mortgage of your new house since 5 months ago. You bought your house then, for $150,000 at a 8 % APR compounded monthly with 25% down payment and the rest mortgage loan from the bank. After your fifth monthly payment you get laid off from your job and even though Bank of Canada has reduced the interest rate to 4% due to economic turndown, you still can’t afford even the new monthly payments. Your neighbor, Madam France, welcomes the opportunity and offers to maintain the monthly payment to the Bank starting from E.O.M 6 in exchange for the ownership of the house. You have no choice other than to accept her offer and handover the ownership to her at E.O.M 5.All monthly payments have taken and will take place in the end of the months i.e. E.O.M.

32. What is the Effective Annual Rate (EAR) for your loan (i.e. before interest rate change)?

a)8%                            b)8.3%                         c)0.69%                       d) none of the above

33. What is the Present value (at t=0) of your 5 payments?

a) 4500                                   b) 112500                                c) 3920.84       d) none of the above

34. What is the Present value (at t=0) of your outstanding debt after 5 payments?

a)146000                                 b)108580                                 c)112500         d) none of the above

35. What is your outstanding debt at E.O.M 5?

a)112265                                 b)108580                                 c)112500         d) none of the above

Explanation / Answer

Solution

8% per annum => 8/12 = 0.67% per month i.e., 0.0067

Part (32)

If a sum P attracts r% interest per month, compounded monthly, the amount at the end one year (i.e., 12 months) = P{1 + (r/100)}12 = P(1.0067)12 in the present case

= 1.08343P => effective interest rate is 8.343% Option (b) ANSWER

Part (33)

Preset value of P obtained after n months = P/(1.0067)n

So, present value of 5 monthly payments = {800/1.0067} + {800/1.00672} + {800/1.00673} +

{800/1.00674} + {800/1.00675} = 3920.84 Option (c) ANSWER

Part (35) 35 is worked out first since this answer is necessary to answer 34

Initial total cost = 150000

Less down payment = 37500 (25%)

Outstanding at the start of month 1 = 150000 – 37500 = 112500

Outstanding at the end of month 1 = 112500 x 1.0067) = 113253.75

Less payment in month 1 = 800

Net Outstanding at the end of month 1 = 112454

Working out this way for 5 months,

Outstanding at the end of month 5 = 112266 Option (a) ANSWER

Part (34)

Present value = 112266/1.00675 = 108579.2 Option (b) ANSWER

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