Here we have a loan at $107,000 at 5.5 % interest rate.

What would the new principal be after the third payment, if the monthly payment was $636?

This is a amortization question.

First,  since we start out with the loan of $107,000, and we know that the interest rate is 5.5 %, we're going to multiply the loan payoff by the interest rate to find out how much interest this borrower is going to pay per year. 

Step 1: $107,000 (initial loan amount) x .055 (interest rate of the loan)= $5885.00 (annual interest paid on a $107,000 payoff)

This is going to be a multi-step process.

What is the monthly interest she will pay for the first month? We divide that 5,885 (annual interest) by 12, and we get $490.41.

Step 2: $5885.00 (annual interest paid) / 12 months = 490.41 first month interest paid

That's how much interest she will pay on this loan during her first payment.

The monthly payment is $636.

Of her $636 monthly payment, $490.41 goes to interest.

We're left with is $145.59 to use toward paying down the loan.

Step 3: $636 monthly payment -$490.41 (first month's interest paid) = $145.59 the amount left over toward the principal of the loan.

$107,000 - $145.59 =  $106,854.41

 Her new payoff on the loan is going to be $106,854.41 after the first payment.

After finding the new principal amount after the first month, we need to move on to the second month's payment.

To find out what she'll owe after the second payment , we start with her new payoff of $106,854.41 and repeat all the process again using the new payoff amount.

$106,854.41 (current payoff of the loan) x .055 (interest rate)= $5876.99 (annual interest paid)

$5,876.99 (annual interest paid) / 12 (months)= $489.74 second month's interest paid

$636 (monthly payment) - $489.74 (interest paid during the second payment) = $146.26 (principal paid down the second month)

$106,854.41 (payoff after first payment) - $146.26 (principal paid during second payment)= $106,708.15 (new payoff after second payment

After finding the principal balance after the second payment, it's time to wrap up with the third and final payment.

To find out what she'll owe after the second payment, we start with her new payoff of $106,708.14 and repeat the process yet again using the new payoff amount.

$106,708.15 x .055 =5,868.94

$5868.94 / 12= $489.07

$636- $489.07 = $146.93

$106,708.15 - $146.93 = $106,561.22 is our final answer.