How to calculate biweekly mortgages manually???

[mtgobsessed]

Hi,

I am familiar with the formula pmt= r/(1-(1+r)^-n).p for calculating mortgage payments on a monthly basis.
I can also figure out how to calculate regular (non accelerated) biweekly mtg pmts on my TI BA II Pluss calculator. I am currently however, struggling to adjust the above manual formula to give me the same biweekly answer as the calculator. Here is the problem i am on: principal of 200000, 5%apr semi annually, 30 years, bi weekly payments.

on the calculator once i set payments/year to 26 and compunding periods to 2 (semi annual) i insert n = 780 (30years x 26 pmts/year) then i put i/y as 5 and pv as 200000 and fv to 0 and i get 492.0917353. I am sure this is correct as all the online mtg calcs get the same pmt.

However!!!! When i do the formula i get a different answer: i first did it this way i divide .05/26=.001923077 to match compounding to payment periods pmt = .0019/ (1-(1.0019)^-780).200000 (i am not rounding when i actually do it. And this gives me 495.28

or i thought maybe i needed to use ear and divide that by 26 so my interest rate was (1+.05/2)^2-1 = .050625 and using that interest rate/26 i got an answer of 498.81

SO...I am confused I need help to make sure i do this right. Online is all just calculators and i want to get the manual concept down please help!

 

[Denis]

> on the calculator once i set payments/year to 26 and compunding periods to 2 (semi annual)
> i insert n = 780 (30years x 26 pmts/year) then i put i/y as 5 and pv as 200000 and fv to 0 and
> i get 492.0917353. I am sure this is correct as all the online mtg calcs get the same pmt.

YES, that is definitely correct...

> However!!!! When i do the formula i get a different answer: i first did it this way i divide
> .05/26=.001923077 to match compounding to payment periods pmt = .0019/ (1-(1.0019)^-780).200000
> (i am not rounding when i actually do it. And this gives me 495.28

NO, you can't do that!

> or i thought maybe i needed to use ear and divide that by 26 so my interest rate was
> (1+.05/2)^2-1 = .050625 and using that interest rate/26 i got an answer of 498.81

NOT QUITE (but you have right idea).
You cannot simply divide the .050625 by 26; that will result in a rate higher than .050625,
since you are compounding 26 times.
You need a rate that when compounded 26 times results in .050625; this way:
(1 + i)^26 = 1.050625 ; 1 + i = 1.050625^(1/26) ; i = .0019012368...
Use that rate and you'll get 492.091735... as payment.

Ya'll ok now?

REMARK:
> I am familiar with the formula pmt= r/(1-(1+r)^-n).p for calculating mortgage payments...

Me no like da way that formula looks (even if correct);
find it easier and clearer to state it this way:

P = A i / (1 - x) where x = 1 / (1 + i)^n (P = Payment, A = Amount borrowed)

 

[mtgobsessed]

Thank You! I know what I was messing up now! Your post was vey helpful.