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 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.