Mr Jones has just bought a house for 250000 He will make a d

Mr. Jones has just bought a house for $250,000. He will make a down payment of 5% on the house, and pay for the rest with a mortgage. The Bank Le Friendly offers 10-year mortgage loans at 13% APR compounded semi-annually, with monthly mortgage payments starting today. What is the amount of Mr. Jones’s monthly mortgage payment?

A. $3,462.31 B. $3,498.84 C. $3,546.13 D. $3,647.40 E. $3,605.56

Solution

A. $3,462.31

Step - 1 .......... Find the Effective annual rate, when compounding is done Semi annually

Effective rate per year = (1.065)² - 1 = 0.134225

Now calculate the monthly rate that equals this annual effective rate.......... Let such monthly interest rate = r

( 1 + r )¹² - 1 = 0.134225

( 1 + r )¹² = 1.134225

1 + r = 12th root of (1.134225) = 1.010551074

r = 0.010551074

Step - 2 ........ we have to find PVIFA ( Present value of Interest factor annuity) when annuity is immediate

This is given by ......... 1 + [ 1 - ( 1 + r ) ^-n ] / r

In the above formula ...... n = number of periods = 10 Years * 12 months = 120. But we have to take only 119, because 1st installment is immediate and for which 1 is added at the beginning of the formula.

= 1 + [ 1 - (1.010551074)^-119 ] / 0.010551074 = 1 + 67.5958303671 = 68.5958303671

Step - 3 .......... Last step

Monthly Installment = Balance / PVIFA = (250000 * 0.95 ) / 68.5958303671 = 3462.31