Question

Karen and Jeremy are purchasing a house and are financing $225,000. The mortgage is a 30-year 4/1 ARM at 3.0% with a 2/6 cap structure. What will the remaining balance be after the first 4 years?

$196,208.00

$210,667.50

$205,335.00

$210,895.73

Answer 1

its a 4year initial term, so define the payments and run a balance

Answer 2

P =

B4 = Bk^(4*12)-P(1-k^(4*12))/(1-k)

Bk^(4*12)-(Bk^(30*12)(1-k)/(1-k^(30*12)))(1-k^(4*12))/(1-k)

225000k^(4*12)-(225000k^(30*12)(1-k)/(1-k^(30*12)))(1-k^(4*12))/(1-k), k=1+.03/12

http://www.wolframalpha.com/input/?i=225000k%5E%284*12%29-%28225000k%5E%2830*12%29%281-k%29%2F%281-k%5E%2830*12%29%29%29%281-k%5E%284*12%29%29%2F%281-k%29%2C+k%3D1%2B.03%2F12

Answer 3

looks like a cut instead of copied my P lol

Answer 4

P = Bk^(30*12)(1-k)/(1-k^(30*12))