To see how monthly payments affect the equity, interest and balance of a loan, let's use an example. We want to take a loan for $2,500.00 for 3 years at 7 per cent interest. First, using the calculator located here, we find the monthly payment is $77.19. The next thing to do is calculate the 7 per cent interest rate as a monthly rate.           .07 ÷ 12 = 0.005833333333...

Let's calculate the results after the first payment.     Interest Paid = Previous Balance * Monthly Interest Rate Interest Paid = $2,500.00 * 0.005833333333 Interest Paid = 14.5833333333 or $14.58 (rounded)     Equity = Monthly Payment -Interest Paid Equity = $77.19 -$14.58 = $62.61     New Balance = Previous Balance -Equity New Balance = $2,500.00 -$62.61 = $2,437.39 ******************************************************************** ********************************************************************

Now for the second payment. Interest Paid = $2,437.39 * 0.005833333333 Interest Paid = $14.218108333 or $14.22 (rounded) Equity = $77.19 -$14.22 = $62.97 New Balance = $2,437.39 -$62.97 = $2,374.42 ******************************************************************** ********************************************************************

Now for the third payment.

Interest Paid = $2,374.42 * 0.005833333333
Interest Paid = 13.85078333254 or $13.85 (rounded)

Equity = $77.19 -$13.85 = $63.34

New Balance = $2,374.42 -$62.97 = $2,311.08

The above calculations are summarized in this table.

Payment #	Payment Amount	Interest Paid	Equity	*** Balance ***
***	******	******	******	$2,500.00
1	$77.19	$14.58	$62.61	$2,437.39
2	$77.19	$14.22	$62.97	$2,374.42
3	$77.19	$13.85	$63.34	$2,311.08

If we were to make line 2, the sum of lines 1 and 2 and
if line 3 was the sum of lines 1, 2 and 3 the results would be:

Payment #	Payment Total	Interest Total	You Own	*** Balance ***
***	******	******	******	$2,500.00
1	$77.19	$14.58	$62.61	$2,437.39
2	$154.38	$28.80	$125.58	$2,374.42
3	$231.57	$42.65	$188.92	$2,311.08

That's fine if you just want to calculate a loan's balance month by month but is there a formula for calculating a loan balance after several months have passed?
Yes, and here's the formula:

Now let's try that third month payment using the above formula.

Remaining Balance = $2,500.00 * (1.005833333333)³ - 77.19 * [((1.005833333333)³-1) ÷ .005833333333]

Remaining Balance = $2,500.00 * 1.0176022818 -77.19 * (0.0176022818 ÷ .005833333333)

Remaining Balance = 2,544.0057045692 - 77.19 * 3.017534023

Remaining Balance = 2,544.0057045692 - 232.9234512377

Remaining Balance = 2,311.08

It's much easier with that formula isn't it?

This is the way the calculator located here performs its calculations.