Final answer:
Using the Present Value formula with a monthly payment of $666, an interest rate of 1% per month, and a loan term of 48 months, the student can borrow approximately $26,280.67 for a new car.
Step-by-step explanation:
The student wants to know how much they can borrow if they can afford a monthly car loan payment of $666 at a market rate of 1 percent per month for 48 months. To solve this, we will use the Present Value (PV) formula for an annuity, which calculates the total loan amount that can be afforded based on periodic payments:
PV = Pmt * [(1 - (1 + r)^-n) / r]
Where,
Pmt = Periodic payment ($666)
r = Periodic interest rate (1% or 0.01)
n = Total number of payments (48)
By plugging in the values into the formula, we get:
PV = $666 * [(1 - (1 + 0.01)^-48) / 0.01]
PV = $666 * [1 - (1.01)^-48] / 0.01
PV = $666 * [1 - 0.60578] / 0.01
PV = $666 * 39.422 / 0.01
PV = $26,280.67
Therefore, the student can afford to borrow $26,280.67, rounded to the nearest penny, with the given terms.