# Finance - Find Monthly Payments (two methods)

• I
• jgiannis
In summary, the conversation discusses the process of calculating monthly "Principal + Interest" for a home loan using both a logical approach and a financial equation. The speaker also mentions a similar calculation for a car loan and questions the difference in calculation between home loans and car loans. The main point of confusion is where the logical approach goes wrong and the speaker affirms their trust in their bank's numbers.
jgiannis
Hi.

I am looking into buying a home. I am trying to calculate the monthly "Principal + Interest." My bank actually provides a neat calculator that removes all of the guesswork (https://www.schoolsfirstfcu.org/wps/portal/Calculator?calculatorParamKey=MortgageCompare).

However, for the fun of math, I tried reaching the same value by using logic in my equation. But it turns out that my equation comes out different than the result from the bank's calculator.

Can anyone explain where my logical approach goes wrong?

Given the following information, here's how I ran the equation, from scratch, using logic:

Total Price of Home: $350,000 Down Payment (20%):$70,000
Principal Loan Amount to be Financed: $280,000 Interest Rate (APR-FIXED): 3.5% Duration of Loan: 30 years Frequency of Payment (monthly): 12 Thus, I figure that if I'm paying 3.5% per year on$280k, then every year I would be paying this much in interest: ($280k)*(0.035) =$9,800.

Thus, in 30 years, the total amount of interest that I would pay is: ($9,800)*(30) =$294,000.

Thus, the total amount of Principal + Interest that I would pay after 30 years would be: ($280,000)+($294,000) = $574,000 Thus, since there are 360 months in 30 years, the monthly cost of Principal + Interest would be: ($574,000)/(360) = $1,594.44. However, using those same numbers, my bank's calculator says that the Principal + Interest would actually be$1,257.33.

I should note that I trust my bank's numbers. I found a finance equation online, and using that equation, I get the same result as my bank. However, the things that puzzle me so much are (a) where did my logical approach go wrong, and (b) what is the logic behind the "correct" financial equation? To me, the "correct" financial equation makes no sense. I do not see the logic in it. Here is the equation that I'm speaking of:

Also, to make things a bit more complicated, I was helping someone calculate a monthly car loan. Here's the given information:

Total Price of Car: $21,000 Down Payment:$7,000
Principal Loan Amount to be Financed: $14,000 Interest Rate (APR-FIXED): 9% Duration of Loan: 5 years Frequency of Payment (monthly): 12 I used the equation above, and I get a value of$290.62. Sounds good.

I also used my own logical approach, and I get a value of $338.33. Also sounds good, but based on the above home loan discussion, I assume this is wrong. The thing that puzzles me this time around is that the car dealership quoted us$338.33. It sounds like they used the same approach as I initially thought of. Why? Is there typically a different calculation in Home Loans vs Car Loans? Thanks for your time.

The $280,000 go down over time, as some part of the$1,257.33 are used to reduce the debts you have. That means interest goes down as well.

If the car dealer asks for \$338.33 they try to rip you off.

As you pay off principal, interest paid goes down, and payments applied to principal go up. And every time (360 payments) you make a payment, the payment gets applied to both principal and interest. But those amounts applied are different each time. In year one, very little is applied to principal. In year 30 almost all of the payment goes to principal.

## 1. How do I calculate monthly payments for a loan?

To calculate monthly payments for a loan, you can use either the Amortization Formula or the Mortgage Formula. The Amortization Formula is: Monthly Payment = Principal * (r * (1 + r)^n) / ((1 + r)^n - 1). The Mortgage Formula is: Monthly Payment = Principal * r * (1 + r)^n / ((1 + r)^n - 1). In these formulas, r represents the monthly interest rate, and n represents the number of months in the loan term.

## 2. What is the difference between fixed and variable interest rates?

Fixed interest rates stay the same throughout the entire loan term, meaning your monthly payments will also remain the same. Variable interest rates, on the other hand, can change over time, causing your monthly payments to fluctuate. It is important to consider the potential risks and benefits of each type of interest rate before choosing a loan.

## 3. Is there a difference between APR and interest rate?

Yes, there is a difference between APR (Annual Percentage Rate) and interest rate. The interest rate is the percentage of the loan amount that you will pay in interest each year. The APR includes not only the interest rate, but also any additional fees or charges associated with the loan, giving you a more accurate representation of the total cost of borrowing.

## 4. How does the length of a loan affect the monthly payment?

The longer the loan term, the lower the monthly payment will be. This is because the principal amount is spread out over a longer period of time, resulting in smaller monthly payments. However, keep in mind that a longer loan term also means paying more in interest over time.

## 5. Can I use a calculator to find my monthly payments?

Yes, there are many online calculators available that can help you find your monthly payments for a loan. These calculators use the Amortization Formula or Mortgage Formula mentioned earlier, making it easy to get an accurate estimate of your monthly payments. Just make sure to input the correct information, such as the loan amount, interest rate, and loan term.

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