n: morgage term in number of years

m: number of years to closing

p: paid point

let t= n *annual_rate

s= m* annual_rate

p is equivalent to an increase of t to d+dt

Assuming no closing cost then

dt ~ c*p

c=t*(exp(t)-1)/(exp(t)-exp(t-s)-s)

So paying point p is equivalent to an increase of annual rate of p*(1/n)*c

example 1:

annual rate = 0.06

term = 30 years

closing until 30 years

t = 0.06*30 = 1.8

s = 0.06*30 = 1.8

c = 1.8 *(exp(1.8)-1)/(exp(1.8)-exp(1.8-1.8)-1.8) = 2.797

suppose paid point is 0.01 (1 point)

then the effective annual rate of this mortgage is

0.06 + 0.01 * (1/30) * 2.797 = 0.06093 = 6.093%

example 2:

Everything same as example 1 except that

closing afte 10 years

s = 0.06*10 = 0.6

c = 1.8 *(exp(1.8)-1)/(exp(1.8)-exp(1.8-0.6)-0.6) = 4.268

then the effective annual rate of this mortgage is

0.06 + 0.01 * (1/30) * 4.268 = 0.06142 = 6.142%

example 3:

Everything same as example 1 except that

closing afte 5 years

s = 0.06*5 = 0.3

c = 1.8 *(exp(1.8)-1)/(exp(1.8)-exp(1.8-0.3)-0.3) = 7.169

then the effective annual rate of this mortgage is

0.06 + 0.01 * (1/30) * 7.169 = 0.06239 = 6.239%

## No comments:

Post a Comment