Solve $130,000 25-yr Mortgage at 4.2%: #8b Unpaid Balance & Interest Paid

[s3a]

For #8b ( https://www.docdroid.net/5W4Imc9/question.pdf ), I don't understand how $104,771.14 is obtained.

#8 re-typed here for your convenience:
A family has a $130,000, 25-year mortgage at 4.2 %, compounded monthly.
a) Find the monthly payment.
b) Find the unpaid balance after 15 years.
c) Find the total amount of interest paid on the mortgage.

In other words, in the solutions pdf ( https://www.docdroid.net/4UqxHKU/answer.pdf ), what's (1+0.00354)^(-180) / 0.00354 supposed to be? (The value 0.00354 is i = (4.25/100)/12 and -n = -15*12 = -180.)

Is the solution incorrect? Is it trying to say $700.63 * (F/A, 0.0425/12, 15*12) = $373,527.03?

Any input that may help me would be GREATLY appreciated!

P.S.
Here are the formulas (for your convenience).:
https://www.me.utexas.edu/~me353/lessons/S2_Evaluation/L02_Equivalence/factor_formulas.html

P.P.S.
If you need more information from me, let me know, and I'll provide it.

 

[tkhunny]

You should try to be very, very much less sloppy.

You have 4.2% and 4.25% listed.

You have 25 years (300 months) and 15 years (180 months) listed.

You WILL have to make up your mind concerning what is wanted.

130,000 @ 4.25% Nominal Annual for 25 Years gives a monthly payment of 704.26.
130,000 @ 4.20% Nominal Annual for 25 Years gives a monthly payment of 700.63.
130,000 @ 4.25% Nominal Annual for 15 Years gives a monthly payment of 977.97.
130,000 @ 4.20% Nominal Annual for 15 Years gives a monthly payment of 974.68.

So, really, what is it that you want? Please decide and then show us your best work. No more chaos.

 

[Wilmer]

c) Find the total amount of interest paid on the mortgage.

SIMPLE: total payments - amount borrowed

You knew that...right??

 

[s3a]

About part a:
About the 4.2 vs 4.25%, oops; sorry about that. The PDF with the question is the "correct question". So, the correct answer for this part is $130,000 * (A/P, 0.0425, 12*25) = $704.26, right?

About part b:
About using 15 years, instead of 25 years, for part b, that wasn’t a typo; I actually meant to do that. The fact that you thought of it as a typo suggests to me that my solution is off for that part (which makes sense, given that I get a negative answer), but my logic, with the $700.63 now corrected to $704.26, was $704.26*(F/A, 0.0425/12, 12*15) = $375,462.29 = F_15 = future value 15 years from the beginning, from which I then subtracted F_15 from $130,000, giving $130,000 – F_12 = $130,000 – $375,462.29 = -$245462.29 (which is negative). What am I doing wrong here?

About part c:
About part c, when I used the $700.63 from the solutions PDF (and it seems that the person who made the solution also made the same mistake as I did (at least as some point in the work), which was assuming that the interest rate is 4.2%, rather than 4.25%), I got an answer that agreed with the solutions in the pdf by doing 12*25*$700.63 - $130,000.00 = $80,189. So, the correct answer is 12*25*$704.26 - $130,000.00 = $81,278, right?

P.S.
When I had initially posted this question, I was only looking for help with part b, as mentioned in the very beginning, but I should probably have emphasized that more. Having said that, now that I’m seeming to get a bunch of different answers than the solutions in the pdf, I’d appreciate it if I could also get confirmations for those (because I don’t want to assume anything wrong before I proceed to other questions).

P.P.S.
What's going on with the formatting of this post, and how can I fix it?

 

[Wilmer]

About using 15 years, instead of 25 years, for part b, that wasn’t a typo; I actually meant to do that. The fact that you thought of it as a typo suggests to me that my solution is off for that part (which makes sense, given that I get a negative answer), but my logic, with the 700.63 now corrected to 704.26, was 704.26*(F/A, 0.0425/12, 12*15) = 375,462.29 = F_15 = future value 15 years from the beginning, from which I then subtracted F_15 from 130,000, giving 130,000 – F_12 = 130,000 – 375,462.29 = -245462.29 (which is negative). What am I doing wrong here?

Well, your 375,462.29 result is way off: should be 176,900.08
Calculation (i = .0425/12): 704.26*[(1+i)^180)-1] / i = 176900.08

Then you need the future value of the 130,000.00:
130000*(1 + i)^180 = 245650.11

So owing after 15 years = 245,650.11 - 176,900.08 = 68,750.03

 

[s3a]

Oops! I used n = 25, instead of n = 15! Sorry for making so many mistakes; it's because I'm not feeling well, but I have to power through it or I will fall behind.

Also, that makes a lot of sense! Thanks!

So, about parts a and c, they are $704.26 and $81,278.00, respectively, right?

 

[Wilmer]

So, about parts a and c, they are 704.26 and 81,278.00, respectively, right?

Yepper! Get well soon...

 

[s3a]

Thanks. :)