Question
Your aunt bought a new car. After three months of car payments she owed a total of $22,275 to the bank for the car loan. After 12 months, she owed $18,900 to the bank for the car loan. What was her average payment rate on the principal of the car loan during this time?
Answers
GPT-4o mini
To find the average payment rate on the principal of the car loan, we can determine how much the loan balance decreased from the time your aunt's loan balance was $22,275 after 3 months to $18,900 after 12 months.
First, we calculate the decrease in the loan balance:
\[
\text{Loan balance after 3 months} = 22,275
\]
\[
\text{Loan balance after 12 months} = 18,900
\]
\[
\text{Decrease in loan balance} = 22,275 - 18,900 = 3,375
\]
Next, we determine the number of months over which this decrease occurred. The decrease happened over 12 months - 3 months = 9 months.
Now, we can calculate the average monthly payment rate on the principal:
\[
\text{Average monthly payment on principal} = \frac{\text{Total decrease in loan balance}}{\text{Number of months}}
\]
\[
\text{Average monthly payment on principal} = \frac{3,375}{9} = 375
\]
Thus, the average payment rate on the principal of the car loan during this time was **$375 per month**.
First, we calculate the decrease in the loan balance:
\[
\text{Loan balance after 3 months} = 22,275
\]
\[
\text{Loan balance after 12 months} = 18,900
\]
\[
\text{Decrease in loan balance} = 22,275 - 18,900 = 3,375
\]
Next, we determine the number of months over which this decrease occurred. The decrease happened over 12 months - 3 months = 9 months.
Now, we can calculate the average monthly payment rate on the principal:
\[
\text{Average monthly payment on principal} = \frac{\text{Total decrease in loan balance}}{\text{Number of months}}
\]
\[
\text{Average monthly payment on principal} = \frac{3,375}{9} = 375
\]
Thus, the average payment rate on the principal of the car loan during this time was **$375 per month**.