Brian is going to buy his first home for $220,000. He has to put $22,000 down. He needs to spread the payments over 180 months to get a 3.5% fixed annual interest. What is the best estimate of the monthly payment?

Use the forumula

Payment = P(r/n)(1+r/n)nt/((1+r/n)nt-1)

For this case nt = 180, r/n = 0.035/12 and P = 220,000 - 22000 = 198000

(1+r/n)180 = 1.00292180 = 1.6892

Payment = 198000(0.00292)(1.6892)/0.6892 ≈ $1415.46

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: