Final answer:
To determine the interest portion of the first payment, the annual interest rate is converted to a monthly rate and multiplied by the principal. For a loan with a $600 principal and a 9.5% annual interest rate, $4.75 of the first $55 monthly payment is allocated to interest.
Step-by-step explanation:
To calculate how much of the first payment on an installment loan will go to interest, you can use the formula for calculating simple interest, which is Interest = Principal × rate × time.
For the given loan, the principal is $600, the interest rate is 9.5% annually, and the time we are interested in is one month.
First, convert the annual rate to a monthly rate by dividing by 12, since there are 12 months in a year.
Monthly interest rate = (Annual interest rate) / 12
Monthly interest rate = 0.095 / 12
Monthly interest rate = 0.0079167
Now, calculate the interest for the first month.
Interest for the first month = Principal × monthly rate × time
Interest for the first month = $600 × 0.0079167 × 1
Interest for the first month = $4.75
So, $4.75 of the first payment will go towards interest. This value should be rounded to the nearest hundredth if necessary, but in this case, it is already denoted to two decimal places.