Calculating the Interest, Equity and Balance of a Loan

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
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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
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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 this 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.

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