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?
- 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.