GARP 2015 Sample Exam, #11, Page 344 P1.T3.

[Dr. Jayanthi Sankaran]

Hi David,

#11 above is as follows:

A homeowner has a 30-year, 5% fixed rate mortgage with a current balance of USD 250,000. Mortgage rates have been decreasing. Which of the following is closest to the amount that the homeowner would save in monthly mortgage payments if the existing mortgage was refinanced into a new 30-year, 4% fixed rate mortgage?

A USD 145
B USD 150
C USD 155
D USD 160

The answer is B and the explanation is:

Total monthly payment = Mortgage payment factor * Principal balance
Mortgage payment factor: r*(1 + r)^n/(1 + r)^n - 1
where r = interest rate and n = the number of payments over the loan term
5% factor = 0.005368216, 4% factor = 0.004774153
Savings = $250,000*(0.005368216 - 0.004774153) = 148.52

How do you get the 5% factor = 0.005368216 and 4% factor = 0.004774153. Plugging in r = 5% and n = 360, into the Mortgage payment factor, I get 5% again. Would be grateful if you would explain

Thanks!
Jayanthi

 

[Deepak Chitnis]

Hi @Jayanthi Sankaran, I dont think we need to do this complicated, you can simply use the TVM function, but if you wanted know:Mortgage payment factor = [rate*(1+rate)^term]/[(1+rate)^term-1]. {0.05/12*[1+0.05/12^360]/[1+0.05/12^360-1]}=0.00417*[4.46774]/[4.46774-1]=0.01863/3.46774=0.00537. (can not give full value because only have 4 decimal on calculator, but I think dont go deep in this now, you can do this easily with TVM function, like, N=360, I/Y=5/12=0.41667,PV= 250,000, then CPT PMT, then simply change the I/Y=4/12=0.33333, but you need try to solve 4% mortgage payment factor.) Hope that helps.
Thank you

 

[Dr. Jayanthi Sankaran]

That's great @Deepak Chitnis - very clear

Jayanthi

 

[David Harper CFA FRM]

Hi @Jayanthi Sankaran where is that question, sorry I cannot find it, it's not in GARP's 2015 Sample Exam that I see?
I totally agree with @Deepak Chitnis, for this, i would just CPT PMT then change the I/Y and re-compute for the difference. This isn't my question, I think it's bad to locate the choices so near to each other. The correct answer is $148.52 yet 145.00 and 150.00 are both choices? That's not ideal because you shouldn't have to spend extra time thinking about the choice if you have the correct answer

 

[Dr. Jayanthi Sankaran]

Hi David,

Yes, totally agree. I don't like the choices either. It is in the 2015 GARP Sample Exam for 'Financial Markets and Products'

Thanks
Jayanthi