Finance
posted by lp on .
You have just purchased a new warehouse. To finance the purchase, you have arranged for a 30year mortgage loan for 80 percent of the $2,800,000 purchase price. The monthly payment on the loan will be $22,000.
a. What is the effective annual rate (EAR) on this loan?

80% of2800000 = 2240000
2240000 = 22000( 1  (1+i)^360)/i
101.81818.. = ( 1  (1+i)^360)/i
101.818182i = 1  (1+i)^360
(1+i)^360 = 1  101.818182 i
Now that is tough equation to solve.
In the "olden days" we used interpolation.
Even Wolfram, at least in its simple version, cannot handle it
http://www.wolframalpha.com/input/?i=solve+1%2F%281%2Bx%29%5E360+%3D+1++101.81x
let's try some values:
i = .04
PV = 22000(1  (1.04)^360)/.04 = 550,000 way off! , expecting appr 224,000
i = .01
PV = 22000(1  1.01^360)/.01 = 2,138,803.28
not bad
i = .0005
PV = 22000(1  1.005^360)/.005 = 3,669.415 , rate is too low
.01 was very close
let i = .0099
PV = 22000(1  1.0099^360)/.0099 = 2,158.164 , even better
let i = .0095
PV = 22000(1  1.0095^360)/.0095 = 2,238,801, a bit too low
let i = .0094
PV = 22000(1  1.0094^360)/.0094 = 2,259794 , a bit too high
do you get the idea?
we could get as close as we want with a good calculator
but the monthly rate has to be between .0095 and .0094
I will guess at .00945
so the effective annual rate is 12(.00945) = .1134
or 11.34%