Final answer:
Joshua needs to find the interest rate that would allow him to repay a $25,000 car loan with annual payments of $6,000 over 5 years. This involves solving for the interest rate in the annuity formula for the given present value, payment amount, and time period.
Step-by-step explanation:
To determine what interest rate Joshua should obtain for his car loan if he wants to make payments of $6,000 per year for 5 years, we need to solve for the interest rate in an annuity formula where the present value is known as well as the payment amount and the number of periods.
The present value (PV) is the value of the car which is $25,000, the annual payment (PMT) is $6,000, and the number of periods (n) is 5 years. The annuity formula we use for this kind of problem is:
PV = PMT [(1 - (1 + i)^-n) / i]
This requires using either a financial calculator or iterative methods to solve for the interest rate (i).
Since the payments are made at the end of each year, this is an ordinary annuity, and we should look for the interest rate that fits this condition, which might require trial and error if a specific formula for solving for interest rate is not available.
Once the exact rate is found, Joshua will know which interest rate he should look for when taking out his loan to be able to make his desired annual payments of $6,000.