You have been living in the house you bought 7 years ago for $300,000. At that time, you took out a loan for 80% of the house at a fixed rate 15-year loan at an annual stated rate of 8.0%. You have just paid off the 84th monthly payment. Interest rates have meanwhile dropped steadily to 6.0% per year, and you think it is finally time to refinance the remaining balance over the residual loan life. But there is a catch. The fee to refinance your loan is $5,000. Should you refinance the remaining balance? How much would you save/lose if you decided to refinance?

Yes, gain $7,287.20

No, lose $12,287.20

Yes, gain $12,287.20

No, lose $7,287.20

What I tried:

I tried calculating like this:

I calculated the interest we are paying currently and balance after 7 years and they are as follows but when I calculate the interest after refinance and calculate profit loss the answers don't match?

240000 * (0.08/12) * (1 + 1/((1 + (0.08/12))^180 - 1) ) =2293.565 --> Current Interest

(2293.565 + (1 + (0.08/12))^(84) * ((0.08/12) * 240000 - 2293.565))/(0.08/12) --> Balance after 7 years == 162242

  • 5
    This looks like a homework question. In order to make any answers more applicable to a wider audience it helps to add more details. What exactly do you need help understanding? What have you tried so far?
    – Nosjack
    Commented Jul 1, 2020 at 18:23
  • @Nosjack, I update what I did. It's not a homework question by the way and it would be great if you could help. Commented Jul 1, 2020 at 18:26
  • 1
    @SarahKaiser Those interest rates are not current market rates which suggests it is a homework problem.
    – Pete B.
    Commented Jul 1, 2020 at 18:58
  • That's not necessarily an exact duplicate, but might provide a useful answer.
    – yoozer8
    Commented Jul 1, 2020 at 18:59
  • @yoozer8, thanks but it doesn't answer my question Commented Jul 1, 2020 at 19:03

1 Answer 1


I don't believe these proposed answers are correct; I match your numbers, and verified with a couple of online calculators. I get a savings of around $10k (after factoring in the $5k cost, varies slightly depending on if you finance this amount or not, but never getting to their numbers).

  • How do you define the amount saved?
    – DJohnM
    Commented Jul 2, 2020 at 4:33
  • [sum of payments in current mortgage] - [sum of payments in refinanced mortgage including the refi fee], no?
    – Joe
    Commented Jul 2, 2020 at 18:11
  • Adding amounts of money at different times is not usually helpful in comparing interest earning/paying scenarios. An alternative: Assuming that the mortgage holder switches to the 6% lender after payment 84, and keeps making the same 2293.55 payments to this lender for 96 months, he can borrow enough to pay off the balance, pay off the penalty, and have 7287.20 extra. Same payments, same mortgage discharged, extra money in hand So the course creators obviously had the cash situation as of payment 84 as the criteria for amount saved/lost...
    – DJohnM
    Commented Jul 2, 2020 at 18:27
  • @DJohnM Why would you assume the payments stay the same? That's not how any mortgage works that I'm familiar with. I suppose you're correct as to what they're assuming, but it's something that absolutely would need to be stated in the question. The normal way you'd do this is to assume the $5k is paid from the refinance funds, meaning if you're not intending to get any net cash out you'd add the $5k to the refinance amount (so refinance 167k instead of 162k), but that's again an assumption (just a more normal one).
    – Joe
    Commented Jul 2, 2020 at 18:31
  • That said, I think what you say is worth an answer, if the question were open - unfortunately it's not; I'd be comfortable with you editing it into mine if you like (and we could CW the answer, also).
    – Joe
    Commented Jul 2, 2020 at 18:33

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