Final answer:
To calculate the monthly payment for a $25,000 car loan at a 6% annual interest rate over 5 years, you convert the annual rate to a monthly rate and use the loan payment formula. The closest given answer to the calculated monthly payment of approximately $483.32 is $471.72 (option a), although none of the provided options match the calculated value exactly.
Step-by-step explanation:
To determine the monthly payment of a $25,000 car loan over a 5-year period with an annual interest rate of 6%, we can use the formula for a fixed installment loan, which is often represented as follows:
M = P \frac{r(1+r)^n}{(1+r)^n - 1}
Where:
- M is the monthly payment.
- P is the principal amount of the loan ($25,000).
- r is the monthly interest rate (annual rate divided by 12).
- n is the total number of payments (number of years times 12).
First, we convert the annual interest rate of 6% to a monthly rate by dividing by 12:
r = 6% / 12 = 0.5% per month
Now, express this percentage as a decimal for calculation:
r = 0.005
We also need to find the total number of monthly payments for a 5-year loan:
n = 5 years * 12 months/year = 60 months
Plugging these values into the formula gives us:
M = $25,000 \frac{0.005 (1 + 0.005)^60}{(1 + 0.005)^60 - 1}
Using a calculator or spreadsheet to do the math, we find that:
M ≈ $483.32
Therefore, the closest answer to our calculated monthly payment from the provided options is $471.72 (option a).
However, the exact calculated value of $483.32 does not completely match any of the given options. This discrepancy could arise from different rounding methods used or from slight variations in the loan terms not specified in the question. Therefore, it is crucial to confirm the details of the loan or use a loan calculator provided by a financial institution to get the precise monthly payment.