Final answer:
To determine the actual rate of a $13,000 loan with an interest rate of 9.6% and three points, one must calculate the upfront cost of the points and the total annual interest. The actual interest rate paid, when accounting for these factors, is approximately 12.6%.
Step-by-step explanation:
To determine the actual rate you would be paying on a $13,000 loan with an interest rate of 9.6% and an additional charge of three points, you need to calculate the total cost of the points and add this to the total interest charged over the life of the loan. One point is equal to 1% of the loan amount, so three points is 3% of $13,000, which equals $390.
Now, you add this upfront cost to the interest that will accumulate over the year. To calculate the interest for one year at 9.6%, you multiply the loan amount by the interest rate: $13,000 * 0.096 = $1,248.
The total cost of the loan is the upfront points plus the interest: $390 + $1,248 = $1,638. To find the actual interest rate, you need to determine what percentage $1,638 is of $13,000. This calculation ($1,638/$13,000) gives approximately 0.126 or 12.6%. Therefore, the actual interest rate you would be paying is about 12.6%.