Question

A home buyer bought a house for $245,000. The buyer paid 20 percent down but decided to finance closing costs of 3 percent of the mortgage amount. If the borrower took out a 30-year fixed-rate mortgage at a 5 percent annual interest rate, how much interest will the borrower pay over the life of the mortgage

Answer 1

Interest = $188,264.78

Step-by-step explanation:

given data

present value = $245,000

rate = 20 %

finance closing costs = 3 percent

time = 30 year

fixed rate mortgage = 5 % annual =
`(0.05)/(12)` monthly

to find out

interest will the borrower pay

solution

we will apply here present value of annuity formula for find annuity that is

present value annuity = Annuity ×
`(1-(1+r)^(-t))/(r)` ..........1

put here value we get

$245,000 × 0.80 × 1.03 = Annuity ×
`(1-(1+(0.05)/(12))^(-30*12))/((0.05)/(12))`

solve it we get

$201,880 = annuity ×
`(0.7762)/(0.0042)`

annuity = $1,083.74

so now we get interest that is

interest = annuity × 360 - present value annuity ..............2

interest = $1,083.74 × 360 - ( $245,000 × 0.80 × 1.03 )

Interest = $188,264.78