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.