Question

A couple wants to buy a $38,000 car and can borrow the money at 8%, paying it off in 3, 4, or 5 years. Find P(4) and write a sentence that explains its meaning.

a) If the car is financed over 4 years, the payment is P(4) = $927.70.
b) If the car is financed over 4 years, the total cost is P(4) = $44,529.
c) If the car is financed over 4 years, the payment is P(4) = $770.
d) If the car is financed over 4 years, the total cost is P(4) = $46,230.

Answer 1

P(4) represents the payment for financing a $38,000 car over 4 years at an 8% interest rate. The value of P(4) is approximately $927.70.

Step-by-step explanation:

P(4) represents the payment for financing a $38,000 car over 4 years at an 8% interest rate. To calculate P(4), we can use the formula for calculating the payment amount on a loan: P = (r * PV) / (1 - (1 + r)^(-n)).

Here, r is the interest rate per period (8% divided by the number of periods in a year), PV is the present value of the loan (38,000), and n is the total number of payment periods (4 years multiplied by the number of periods in a year).

Plugging in the values, P(4) = (0.08/12 * 38000) / (1 - (1 + 0.08/12)^(-4*12)).

After solving the equation, we find that P(4) is approximately $927.70.