Question

You are ready to buy a house, and you have $40,000 for a down payment and closing costs. Closing costs are estimated to be 6% of the loan value. You have an annual salary of $60,000, and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly income. The interest rate on the loan is 4% per year with monthly compounding for a 15-year fixed rate loan. What is the down payment for the house? (Choose the nearest value) a. $11,356.14. b. $18,643.86. c. $28,643.86. d. $21,356.14.

Answer 1

c. $28,643.86

Step-by-step explanation:

For computing the down payment we need to do following calculations which are shown below;

Since annual salary is $60,000 so monthly salary is

= $60,000 ÷ 12 months

= $5,000

And, the monthly mortgage payment equal to 28% of monthly income i.e

= $5,000 × 28%

= $1,400

Now the present value is

= $1,400 × {1 - (1 ÷ 1 + 0.003333 )^180} ÷ 0.003333

= $1,400 × 135.1822927

= $189,255.2098

The 4% is annual rate so monthly rate is 0.003333

And, monthly year is

= 15 years × 12 months

= 180 months

And, closing cost is 6% of the loan value i.e

= $189,255.2098 × 6%

= $113,55.31259

Now the down payment is

= $40,000 - $113,55.31259

= $28644.69 i.e $28,643.86 approx

We simply do the above calculations so that the down payment could come