Fully amortized loan first month payment

Borrower Smith receives a fully amortized loan for $130,000 with an interest rate of 5.5% for 30 years.  His monthly payments are $873.54.

What is the balance of the principal after the first month’s payment?

  1.  $129,404.16
  2.  $129,722.30
  3.  $129,126.46
  4.  None of the above

C is the answer.

Remember that if a loan is amortized, then the monthly payments will include both interest and principal.

On a $130,000 loan, with a 5.5% interest rate, the interest being paid every year is $130,000 * .055 = $7,150.  This means every month he pays $7,150/12 = $595.84 in interest.

He only pays $873.54 in his first month, out of which $595.84 is interest.  This means that he only pays $873.54 – $595.84 = $277.70 in principal, which means that the balance of the principal after the first month is $130,000 – $277.70 = $129,722.30.