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## How to Compute the Remaining Balance on a Loan

**By JLP** | June 14, 2006

Did you know that there is a formula that will tell you the remaining balance on a loan? There is and I am going to show you how to perform the calculation.

**For Example**

Let’s say you took out a $25,000/60 month (5 years) loan with a 7% interest rate to buy a car. Your monthly payment is $495.03. You have made 12 payments on the loan and you want to know what your loan balance is. To perform this calculation, you need to use this scary-looking formula:

Filling in the information that we have, the formula looks like this:

Did you get all that? If your answer was different from mine, it is due to rounding. However, your answer should be pretty close to the answer I got. So, this tells us that 12 months into the $25,000 loan, you still owe over $20,672.

If you didn’t understand this, don’t worry. I created **The Remaining Loan Balance Calculator** to help you out.

**Topics:** Financial Math Basics | 5 Comments »

June 16th, 2006 at 2:38 am

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June 16th, 2006 at 5:31 am

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June 17th, 2006 at 5:06 pm

I don’t know if it is appropriate to post a question in here. Please forgive me if this is a breach of etiquette, but I’m new to this and only discovered your blog this afternoon. I would be very grateful for a bit of advice.

I’m 44 and would like to retire at 65. The problem is that

I have student loans that total approximately $110,000 with an interest rate of 6.125% (the rate will go down to 5.125% in about two and a half years). I’m currently paying $740 per month and the loans should be paid off in about 28 years, more or less.

I am also currently putting $600 per month into various mutual funds which I planned to use to supplement my retirement benefits and social security benefits (if there are any).

Should I direct some of the money I’m putting into the mutual funds towards the principle of my studnet loan? I only make $64,000 per year so the $600 I’m investing is about all that I have left after paying living expenses.

Thank you for your consideration.

Steve

July 22nd, 2006 at 4:16 pm

Hi, there’s actually a typo in the formula, although the example was computed correctly:

For brevity, let’s have

A = amount borrowed

P = payment

I = i / (12 * 100)

The formula as shown above is:

A * (1+I)^n – [ P/I * (1+I)^n - 1 ]

It should instead be stated as:

A * (1+I)^n – [ P/I * ( (1+I)^n - 1 ) ]

March 6th, 2011 at 7:18 am

Melvin’s equation as well as the one published are correct from a syntax point of view, as the second term [P/I*((1+I)^n-1)] is redundant to [P/I*(1+I)^n-1]as the proper order of operation in mathematical calculations are as follows:

Starting from left to right the inner most parentheses must be calculated first from left to right with exponentiation first in the order they appear, followed by multiplication or division in the order they appear followed lastly by addition or subtraction in the order they appear.Thus 1+I must be calculated first followed by raising that result to the Nth power. Then going back from the left P/I is calculated followed by the multiplication the exponentiated previous result and last subtracting 1. The adding extra brackets does help those that are not familiar with the true order of operations in mathematics but a computer will yield correct and same answer every time for both equations.