A person was considering buying a house priced at $350,000. A mortgage company c

Question

A person was considering buying a house priced at $350,000. A mortgage company claimed the interest rate for the 20-year loan is 3.5%. The company also estimated that the points and Appraisal, Credit Report, Processing, Document Preparation, Administration, Underwriting, Flood Certificate, Tax Service, Wire Transfer, and other fees would be $13,000 in total.

a) What would be the monthly payment, if the person decided to borrow 90% of the cost of the house and 100% of the processing fees?

b) What is the APR of the loan?

c) If the person accepts the terms of the loan on Feb. 28, 2010, the first monthly payment is due on March 31. How much mortgage would be paid off after the payment on January 31, 2015?

d) How much interest charge could this person claim for deduction in the 2014 Tax Return, i.e. the total interest occur during year 2014?

Explanation / Answer

a Amount of loan taken = 90% of price of house + 100% processing fees = 90% of 350,000 + 100% of 13,000 = 315,000 + 13,000 = $ 328,000 rate of interest = 3.50% per annum, i.e. 0.292 % per month Cumulative annuity for 20 years with monthy rest with above interest rate = 172.4197 Therefore, monthly instalment amount is = Loan amount / annuity amount = 328000 / 172.4197 = $ 1,902.33 b APR of loan the interest rate for monthly payment of $ 1,902.33 for an amount of $ 315,000 is the APR of loan Cumulative Annuity for 20 years with monthly rest = = 315000/1902.33 = 165.5864 From annuity table we get 0.25% for a value of 180.3109 and 0.40% for a value of 154.0933 Thus, interpolating the % for the value of 165.59, we get = 0.25% + (0.40% - 0.25%) * [(180.3109-165.5864) / (180.3109 - 154.0933) ] = 0.3342 % for yearly rate we get = 0.3342 *12 = 4.01% Thus, APR of loan is 4.01 % c Loan acceptance date, Feb 28, 2010 First date of payment, March 31, 2010 No. Of payments till Jan 31, 2015 = 59 instalments Mortgage paid off till jan 31, 2015 = = Monthly payment * Cumulative annuity for 59 periods at 0.2916 % ( 3.50% / 12) = 1902.33 * 54.1298 = $ 102,972.74 d For the year 2014, period comes out to be from period 47 to period 58 Mortgage paid off in the year 2014 = = Monthly payment * (Cumulative annuity for 47th to 58th periods at 0.2916 %) = Monthly payment * (Cumulative annuity for 58th periods less 46th period) = 1902.33 * (53.2877 - 42.9888) = 1902.33 * 10.2989 = $ 19,591.91 Total amount paid in 2014 = = $ 1,902.33 * 12 = $ 22,827.96 Therefore, interest amount = = Total paid less mortgage paid off = 22,827.96 - 19,591.91 = $ 3,236.05

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