Mortgage refinance

[hellohi]

hello @David Harper CFA FRM

In financial markets and products topic practise question in official GARP book, they ask the following question:

A homeowner has 30-year, 5% fixed rate mortgage with a current balance of USD 250000. 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 was B.

may you give the simplest way to solve this question?

thanks

 

[brian.field]

This is a simply math problem - it requires you to know how to calculate the payment on a fully amortizing loan. You can use the PMT function in excel, even easier, just use the TVM functionality on the BAII Plus calculator.

N = 12*30 = 360 (months)
5% / 12 = period rate
PV = 250000
FV = 0
solve for PMT

then repeat using adjusted rate of 4% / 12 and examine the difference in the resulting PMT amounts.

I might have a few items slightly off but this is the generally easiest method...

 

[hellohi]

This is a simply math problem - it requires you to know how to calculate the payment on a fully amortizing loan. You can use the PMT function in excel, even easier, just use the TVM functionality on the BAII Plus calculator.

N = 12*30 = 360 (months)
5% / 12 = period rate
PV = 250000
FV = 0
solve for PMT

then repeat using adjusted rate of 4% / 12 and examine the difference in the resulting PMT amounts.

I might have a few items slightly off but this is the generally easiest method...

dear brian

thanks for help

but really I solved it according your steps and did not get the exact answer

 

[rajivpro]

Please follow the following steps on your BA II Plus calculator:
1) Press 2nd & the FV key --> Clear TVM
2) Press 30 & N, 5 & I/Y, 250,000 & PV, 0 & FV --> CPT & PMT = 16262.86
3) Press 2nd & the FV key --> Clear TVM
4) Press 30 & N, 4 & I/Y, 250000 & PV, 0 & FV --> CPT & PMT = 14457.52
5) Press 2nd & the FV key --> Clear TVM
6) Savings --> (16262.86 - 14457.52)/12 = 150.45

Hope this is the approach to be followed.

 

[Mkaim]

dear brian

thanks for help

but really I solved it according your steps and did not get the exact answer

I am surprised that the text doesn't cover this (or David's videos). Anyways, see my version below.

BA II Instructions
Step 1
N = Number of total payments = Years * Months = 30 X 12 = 360
I/Y = Periodic interest rate = One period in this case is one month, but the rate is quoted in annual terms so we have to divide--> 5/12 = .416667 (Make sure the you don't enter the rate in decimal (%) terms).
PV = Amount you're going to finance = -$250,000 (Make sure you enter this as a negative value)
FV = 0 --> Because we're not compounding.
PMT = Solve --> Press CPT and then PMT.

Step 2
Leave everything as is and just change the rate--> again, by dividing the annual rate, 4% in this case, by 12 --> Enter 4/12 = .3333-->Solve for payment [-->Press the "=" sign-->Press "I/Y"-->Press CPT-->Press PMT]

 

[hellohi]

Please follow the following steps on your BA II Plus calculator:
1) Press 2nd & the FV key --> Clear TVM
2) Press 30 & N, 5 & I/Y, 250,000 & PV, 0 & FV --> CPT & PMT = 16262.86
3) Press 2nd & the FV key --> Clear TVM
4) Press 30 & N, 4 & I/Y, 250000 & PV, 0 & FV --> CPT & PMT = 14457.52
5) Press 2nd & the FV key --> Clear TVM
6) Savings --> (16262.86 - 14457.52)/12 = 150.45

Hope this is the approach to be followed.

dear it is great help, thanks a lot

 

[hellohi]

I am surprised that the text doesn't cover this (or David's videos). Anyways, see my version below.

BA II Instructions
Step 1
N = Number of total payments = Years * Months = 30 X 12 = 360
I/Y = Periodic interest rate = One period in this case is one month, but the rate is quoted in annual terms so we have to divide--> 5/12 = .416667 (Make sure the you don't enter the rate in decimal (%) terms).
PV = Amount you're going to finance = -$250,000 (Make sure you enter this as a negative value)
FV = 0 --> Because we're not compounding.
PMT = Solve --> Press CPT and then PMT.

Step 2
Leave everything as is and just change the rate--> again, by dividing the annual rate, 4% in this case, by 12 --> Enter 4/12 = .3333-->Solve for payment [-->Press the "=" sign-->Press "I/Y"-->Press CPT-->Press PMT]

thanks dear Mkaim for help,

the reult was 148.6 it is closest to 150, so the answer is 150.
I did not know how to apply this [Press the "=" sign-->Press "I/Y"-->Press CPT-->Press PMT] to get the result as 148.6 without subtract outcomes from each other.
may you clarify more this concept : FV = 0 --> Because we're not compounding. In some cases I notecd that PV or FV be zero (0) and some cases I saw they left empty, I mean they ignord in the calculation, so if you can to give me an example at what case i should to fill with 0 and what case I should to leave them empty and ignord?

thanks
great help

 

[ShaktiRathore]

Hi,
monthly mortgage payments=MP=(MB0*r)/(1-(1+r)^-T) where r is the monthly rate and T is the time in months
Thus change in MP for change in r from r1->r2=MB0*((r2/(1-(1+r2)^-T))-(r1/(1-(1+r1)^-T)))
MB0=250000 and T=30*12=360 ,r1=5%/12=.004167,r2=4%/12=.003333
change in Monthly payment when r changes as 5%->4% =250000*((.003333/(1-(1+.003333)^-360))-(.004167/(1-(1+.004167)^-360)))=-148.6~-150 thus decrease in MP by 150.
thanks

 

[hellohi]

Hi,
monthly mortgage payments=MP=(MB0*r)/(1-(1+r)^-T) where r is the monthly rate and T is the time in months
Thus change in MP for change in r from r1->r2=MB0*((r2/(1-(1+r2)^-T))-(r1/(1-(1+r1)^-T)))
MB0=250000 and T=30*12=360 ,r1=5%/12=.004167,r2=4%/12=.003333
change in Monthly payment when r changes as 5%->4% =250000*((.003333/(1-(1+.003333)^-360))-(.004167/(1-(1+.004167)^-360)))=-148.6~-150 thus decrease in MP by 150.
thanks

thanks dear you are creative

 

[Nicole Seaman]

Hello @hellohi

This question was also answered by another member and David in another thread: https://forum.bionicturtle.com/threads/garp-2015-sample-exam-11-page-344-p1-t3.9124/#post-38381. If you use the search function, copy and paste the first part of the question in the search box. For example, I pasted this into the search box: A homeowner has 30-year, 5% fixed rate mortgage with a current balance. It brought the other thread right up.
Thank you,

Nicole

 

[hellohi]

Hello @hellohi

This question was also answered by another member and David in another thread: https://forum.bionicturtle.com/threads/garp-2015-sample-exam-11-page-344-p1-t3.9124/#post-38381. If you use the search function, copy and paste the first part of the question in the search box. For example, I pasted this into the search box: A homeowner has 30-year, 5% fixed rate mortgage with a current balance. It brought the other thread right up.
Thank you,

Nicole

I think the person who answer there called deepak and I am sure that the answer there shortage, and need some modification.

 

[Mkaim]

thanks dear Mkaim for help,

the reult was 148.6 it is closest to 150, so the answer is 150.
I did not know how to apply this [Press the "=" sign-->Press "I/Y"-->Press CPT-->Press PMT] to get the result as 148.6 without subtract outcomes from each other.
may you clarify more this concept : FV = 0 --> Because we're not compounding. In some cases I notecd that PV or FV be zero (0) and some cases I saw they left empty, I mean they ignord in the calculation, so if you can to give me an example at what case i should to fill with 0 and what case I should to leave them empty and ignord?

thanks
great help

I think the person who answer there called deepak and I am sure that the answer there shortage, and need some modification.

Sorry, but I don't understand what you just wrote. Can you please clarify?

 

[Mkaim]

thanks dear Mkaim for help,

the reult was 148.6 it is closest to 150, so the answer is 150.
I did not know how to apply this [Press the "=" sign-->Press "I/Y"-->Press CPT-->Press PMT] to get the result as 148.6 without subtract outcomes from each other.
may you clarify more this concept : FV = 0 --> Because we're not compounding. In some cases I notecd that PV or FV be zero (0) and some cases I saw they left empty, I mean they ignord in the calculation, so if you can to give me an example at what case i should to fill with 0 and what case I should to leave them empty and ignord?

thanks
great help

hmmmm.... I'll let you do some basic internet search and figure this out. Hint...you can use Youtube, Google, and many other internet sources. By the way, you should know this by now.

 

[Deepak Chitnis]

Hi @hellohi as I stated in that thread I don't think understanding the mortgage payment factor is not important. At that time I made some my research (because I was not only learning for the exam, I was getting deep dive), for exam just be sure that you understand the concept clearly, understanding the maths behind that is not important. Just make sure to understand the concept. I dont think exam will ask you to calculate mortgage payment factor.
Thank you

 

[hellohi]

hmmmm.... I'll let you do some basic internet search and figure this out. Hint...you can use Youtube, Google, and many other internet sources. By the way, you should know this by now.

thanks
Ill do my best on the net and ill tell you
thankssssss

 

[hellohi]

Hi @hellohi as I stated in that thread I don't think understanding the mortgage payment factor is not important. At that time I made some my research (because I was not only learning for the exam, I was getting deep dive), for exam just be sure that you understand the concept clearly, understanding the maths behind that is not important. Just make sure to understand the concept. I dont think exam will ask you to calculate mortgage payment factor.
Thank you

you are great dear
thanks a lot and I am sorry
understand the concept more important than math
did you finish part 1?

 

[Deepak Chitnis]

Hi @hellohi, I finished part 1 last November, if you are only going for the exam dont need to get deep dive into it, I think it is a simple TVM function nothing more just study the concept very well and please try to post your query in specific thread you dont need to create new thread all the time. It cost so much time to @David Harper CFA FRM and @Nicole Manley to clean forum.
Thank you

 

[hellohi]

Hi @hellohi, I finished part 1 last November, if you are only going for the exam dont need to get deep dive into it, I think it is a simple TVM function nothing more just study the concept very well and please try to post your query in specific thread you dont need to create new thread all the time. It cost so much time to @David Harper CFA FRM and @Nicole Manley to clean forum.
Thank you

dear @Deepak Chitnis

Thank you very much, but you were not forced to tag David and Nicole

 

[Deepak Chitnis]

Hi @hellohi it helps them to delete unwanted content. There are so many people who create tons of thread and don't visit them ever. It is for there note so can easily clean this.
Thank you

 

[Apara]

Hello,

Can someone please help me with this MBS question.

A homeowner has a 30 year 5% fixed rate mortgage, with a current balance of USD 250,000. Mortgage rates have been decreasing. If the existing mortgage is refinanced into a new 30 year 4% fixed rate mortgae, how much will the homeowner save monthly.

I know the formula i.e. r (1+r)^n / (1+r) but I am not getting the answer. I do not have access to your forum, hence couldn't check if anyone else has asked this question.