« “Why Would the Interest Portion of My Car Payment Fluctuate from Month to Month?” | Main | Out of the “Office” »

## Financial Formulas Everyone Should Know – How to Calculate a Loan Payment

**By JLP** | May 5, 2010

Let’s say you want to buy a house. You need to finance $200,000 for 30 years and your interest rate is 5% per year. Do you know how to calculate your monthly payment?

Sure, you could go to an online calculator but it’s also good to know the formula. To make this particular calculation, you need this formula:

Where…

Principal = $200,000

Rate = .05 ÷ 12 or .0041667

N = Number of payments (360)

Now I’ll walk you through the calculation:

I ran the calculation in Excel, and it game me a payment of $1,073.64. The one penny difference is due to rounding.

The cool thing about this formula is that it works on any kind of loan as long as you make the proper adjustments. You would do yourself well to learn this formula or at least know how to use a financial calculator the next time you purchase a car.

**Topics:** Financial Math Basics | 12 Comments »

May 5th, 2010 at 10:46 am

Might as well put out the total cost of this $200,000 home after the interest has been added on – $386,514. Even now, it would be hard to get much of a home for $200,000 in California.

May 5th, 2010 at 10:57 am

Actually, the total cost is less than that due to inflation.

May 5th, 2010 at 12:15 pm

In comment 2, JLP is pointing out that it doesn’t make any sense to add monetary amounts that have different dates on them without discounting each amount to present value. How about the formula for that, JLP?

May 5th, 2010 at 1:05 pm

I’m not sure of the formula for that exact calculation but it is simply discounting each payment by a monthly inflation factor. In this case I used a monthly inflation rate of .2466%. I discounted each payment using this formula:

1,073.65 ÷ 1.002466^{month #}So, the calculation for the 24th payment would look like this:

1,073.65 ÷ 1.002466^{24}You should get something close to 1,012.01.

The reasoning for this is that while your payment on a fixed mortgage stays constant, inflation is eating away at the value of the dollars used to pay the mortgage.

When I do that for all 360 payments and sum them, I get $255,980.30 as the total cost of the payments.

May 5th, 2010 at 2:17 pm

I don’t have an understanding of that. Are you saying that the dollars paid total to a different number than your ending total cost? It looks like you’re discounting the value of the money paid, but it doesn’t change the number of dollars going out.

May 5th, 2010 at 2:24 pm

Yes, you are paying out $386,514 but it’s less than that when you factor in inflation. Just like how a person might desire $1,000,000 at retirement. If retirement is 30 years away, and they don’t adjust that $1 million goal upward to account for inflation, they may have $1 million but it will only be worth $300,000 thirty years from now. Inflation works against you in saving money but for you in paying a fixed payment.

May 5th, 2010 at 2:30 pm

wow love the math guys, havent seen this since my college days. definitely cool to see, but with technology the way it is, no one needs to know this anymore, just google loan calculator, and type in the data, and bang its done. i know its a shame, slowly dumbing down our population, but its too convenient

May 5th, 2010 at 2:48 pm

#7 Stephan) I agree — financial math is complicated stuff, and 99.9% of the population doesn’t actually need to know how to perform the calculations. They do need to know, however, what the inputs into the formulas mean and how drastic the results are affected based on slight changes in input (interest rate, num_payments, etc).

May 6th, 2010 at 9:47 am

You may use a tool such as this:

http://www.miniwebtool.com/amortization-calculator/

May 7th, 2010 at 7:53 am

Excellent piece of information. I use Excel PMT formula for all the calculations but have been searching to get a ‘manual’ formula to do it myself (when in front of agent, with no PC and with basic calculator which has “to the power of” feature). Thanks for the valuable information.

May 10th, 2010 at 12:44 pm

Thanks for sharing this with me! I feel like I’m back in high school math class (in a good way). It’s always important to have an understanding of what is happening to your money (and if buying at $200,000 house is feasible).

May 10th, 2010 at 4:07 pm

” but with technology the way it is, no one needs to know this anymore”

The devil’s in the details. Everyone should understand the fundamentals of the time value of money, and it doesn’t hurt to understand the basics of finance. This affects all of us. Or at least most of us.

Usually, most people that don’t understand this are the ones that need this most.