Tuckman Fixed Rate Mtg. Payment - Example in Reading

[joshsmith0221]

Hi All,

I am reviewing the formulas within the reading for mortgage fixed payment and I am unable to match the calculation amounts. Hopefully someone can clarify they are getting the same result. I see two items that are giving me pause.

The second graphic below (bottom of page 6 in the reading) has a 1- after the summation term, whereas the top graphic (top of page 5) does not. When adding the 1- to the top formula, I come up with a value of ~12ok.

Top Formula - Calculation without 1-
477.42*360*(1/(1+(.04/12))^360) = 100,000
477.42*360*0.30179586515 = 100,000
51870.0174984 = 100,000

Top Formula - Calculation with 1-
477.42*360*[1-(1/(1+(.04/12))^360)] = 100,000
477.42*360*0.69820413484 = 100,000
120001.1825 = 100,000




I checked the PDF again to ensure I hadn't overlooked any raised revisions, so hopefully someone can advise if I am making a mistake, or if there are indeed inconsistencies above.

Thanks in advance.

Best,
Josh

 

[Praveen_India]

Hi Josh,

Please try using Calculator for this:

Since the outstanding balance is PV of the future monthly EMIs, we can calculate required values as below:

1. PV=100,000, N=12*30=360, I/Y=4/12, CPT PMT

2. N=25*12, I/Y=4/12, PMT= 477.41, CPT PV (now its only for 25 years)

Thanks,
Praveen

 

[ShaktiRathore]

Hi
Formula with 1- is correct. We are addign Pvs of MP 477.42 over T months to arrive at o/s principal so,
Sigma(n=1 to T)MP/(1+r/12)^n=MP/(1+r/12)+ MP/(1+r/12)^2+....+ MP/(1+r/12)^T is gp with first term MP/(1+r/12) and cr=1/(1+r/12)so Gp sum=a(1-cr^T)/(1-cr)=[ MP/(1+r/12)]*(1-(1/1+r/12)^T)/ (1-1/(1+r/12))( =(MP*12/r)* (1-(1/1+r/12)^T)
Sigma(n=1 to T)MP/(1+r/12)^n= (MP*12/r)* (1-(1/1+r/12)^T) so both 1- and w/o 1- are same.
For MP=477.42 ,T=360
477.42*360*(1/(1+(.04/12))^360) = 100,000 is incorrect u mistook n for T and forgot ti include Sigma.
Correct is 477.42*(12/.04)*(1-(1+(.04/12))^360) = 100,000=100,000
Thanks

 

[joshsmith0221]

Ok, thank you for the suggestion Praveen. I do feel comfortable with the BA II Plus route, just wanted to make sure I had a grasp on the actual formula.

Thanks Shakti, I see my error now.

Good day to you both.