Final answer:
To calculate how much car you can afford with a $450 monthly payment over 5 years at 6% APR, use the present value of an annuity formula. Convert the APR to a monthly rate and use the total number of months to find the total loan amount you can afford.
Step-by-step explanation:
When determining how much car you can afford with a monthly payment of $450 over a 5-year period at a 6% APR, you are essentially calculating the present value of an annuity. This type of calculation considers the total amount of money you can borrow given the interest rate and the length of time over which you will pay back the loan. To do this, use the formula for the present value of an annuity:
PV = PMT × [(1 - (1 + r)^-n) / r]
Where:
- PV is the present value or the amount of money you can afford to borrow.
- PMT is the monthly payment which is $450.
- r is the monthly interest rate (APR divided by 12).
- n is the total number of payments (months).
First, convert the annual interest rate to a monthly rate by dividing by 12. So, r = 6%/12 = 0.5% or 0.005 in decimal form. Since you're paying over 5 years (60 months), n = 60. Plugging in these numbers gives us: PV = $450 × [(1 - (1 + 0.005)^-60) / 0.005]
Calculating the above will give you the total loan amount that you can afford.