Find the amount applied to principle for the third month of a 4-year loan of $10 comma 900 which charges 3.4 percent compounded monthly with monthly payments.

  $211.18

Step-by-step explanation:

Monthly payments are computed using the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12·t))

  = $10,900(.04/12)/(1 -(1 +.04/12)^(-12·4)) ≈ $246.11

First payment

The monthly interest rate is 1/3%, so the interest due is ...

  $10,900 × 1/300 = $36.33

The loan balance after the first payment is ...

  $10,900 +36.33 -246.11 = $10,690.22

Second payment

The interest due is ...

  $10,690.22 × 1/300 = $35.63

The new balance after the payment is ...

  $10,690.22 +35.63 -246.11 = $10,479.74

Third payment

The interest due is ...

  $10,479.74 × 1/300 = $34.93

The amount of the payment that will be applied to principal is the difference between the payment amount and the interest charge:

  amount to principal = $246.11 -34.93 = $211.18