I'm really not good at math. So please forgive me for this noob question that I have.. Just trying to learn basic percentage calculation with money lending..

Here's an example of how the APR works. You see an advertisement offering a 30-year fixed-rate mortgage at 7 percent with one point. You see another advertisement offering a 30-year fixed-rate mortgage at 7 percent with no points. Easy choice, right? Actually, it isn't. Fortunately, the APR considers all of the fine print.

Say you need to borrow $100,000. With either lender, that means that your monthly payment is $665.30. If the point is 1 percent of $100,000 ($1,000), the application fee is $25, the processing fee is $250, and the other closing fees total $750, then the total of those fees ($2,025) is deducted from the actual loan amount of $100,000 ($100,000 - $2,025 = $97,975). This means that $97,975 is the new loan amount used to figure the true cost of the loan. To find the APR, you determine the interest rate that would equate to a monthly payment of $665.30 for a loan of $97,975. In this case, it's really 7.2 percent.

from howstuffsworks

How to calculate the interest rate that would equate to a monthly payment of $665.30 for a loan of $97,975 in 360 months?

What is the formula for this?

  • The advertised APR assumes that you keep the loan for the full 30 years; never have a late charge; never have a pre-payment penalty; and never re-finance. If you pay off the loan ahead of schedule, your effective average interest rate will be higher, because the closing costs will be spread out over less time. The advertised APR also does not account for your money that is tied up in the escrow account, not earning any interest.
    – Jasper
    Commented Dec 8, 2015 at 20:33

1 Answer 1


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Let's start by saying that of all the things to solve in a mortgage equation, the rate is the toughest. It's the least friendly to solving with pencil and paper. While I never tire of expressing my love for my Texas Instruments BA-35 financial calculator, it's no longer in production, and most folk won't have access, but Excel is right there.

The financial function pops up for you with RATE as a choice for solving.

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I filled in the cells to show the numbers. The -665.30 is a typical convention for money flows as it's a payment from you not a credit for interest you earn. Note, some mortgage calculators leave this entry as positive. It takes a second to see how one's calculation or spreadsheet does this.

Last, you can see the software wants a "guess." This is because the software has a loop, guessing and getting closer to the solution. I entered .005 to guess 6% per year. The correct solution is .006 or 7.2% per year.

Class dismissed.

  • Wait! My Excel doesn't have those funny blue scroll bars? (Seriously, thank you for a great answer)
    – MrChrister
    Commented Sep 16, 2012 at 16:08
  • Funny. How's this? (Disclaimer - PC users may not see the blue scroll bars. I am on a Mac.) Thank-you for the kind words. I was afraid I got carried away with the level of detail, but maybe not, I hope OP returns to see how to run the numbers. Commented Sep 16, 2012 at 17:55
  • I still don't understand.. I don't use excel so I don't know how to do this...
    – Kevin Lee
    Commented Oct 5, 2012 at 16:24
  • My understanding is that unlike calculating the payment, given the other details, calculating the rate is not straightforward. A rate is guessed, and moved up or down until the number is found. You guess the rate, calculate payment, and lower or raise the rate until the payment is correct to the penny. Commented Oct 5, 2012 at 20:11
  • Also, some scenarios can have more than one rate. For example, if the borrower receives large amounts of cash at different times (especially before and after making payments), there can be different rates that solve the equation. The initial guess encourages the program to find an answer close to the guess.
    – Jasper
    Commented Dec 8, 2015 at 20:38

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