A person considering buying a house priced at $200,000. A mortgage company claim

Question

A person considering buying a house priced at $200,000. A mortgage company claimed the interest rate for the 20-year loan is 5.5%. The company also estimated that the points and Appraisal, Credit Report, Processing, Document Preparation, Administration, Underwritting, Flood Certificate, Tax Service, Wire Transfer, and other fees would be $12,000 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 of the principal would be paid off after the payment on May 31, 2011?
d) How much interest charge could this person claim for deduction in the 2011 Tax Return, i.e. the total interest occur during year 2010?

Explanation / Answer

If the person accepts the terms of the loan,

the total amount borrowed = 200000 + 12000 = 212000

interest = 5.5 %

No. of monthly payments, N = 20*12 = 240

r = (5.5/12)/100

Monthly payment = r * P/(1 - (1+r)^-N) =(5.5/12)/100*212000/(1 - (1+(5.5/12)/100)^-20)

C = $ 1458.32

(c)

To find principal amount paid of we need to calculate the outstanding loan balance.

Outstanding loan balance Bk i.e, k is any point in time is

Bk = P ( 1 + i )^K - C ( (1+i)^k-1 + (1+i)^k-2 + ..... + 1)

given P = 212000

C = 1458.32

k = 15

i = (5.5/12)/100

B15 = 212000 *( 1 + (5.5/12)/100)^15 - 1458.32 * ( ( 1 + (5.5/12)/100)^15 - 1)/((5.5/12)/100)) = $ 204 461.28

Principal amount piad off = principal - Outstanding balance = 212000 - 204461.28 = $ 7538.72

(d)

The interest paid in 2010 is = Total amount paid - ( Principal - Outstanding balance)

Bk = P ( 1 + i )^K - C ( (1+i)^k-1 + (1+i)^k-2 + ..... + 1)

here k = 10

B10 = 212000 * ( 1 + (5.5/12)/100)^10 - 1458.32 * ( ( 1 + (5.5/12)/100)^10 - 1)/((5.5/12)/100)) = 207031.86

Interest paid = 10 * 1458.32 - ( 212000 - 207031.86) = $ 9615.06

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