Question

Jojuan wants to buy a used car for $12,000 but can only afford $200 a month. What interest rate would he need to find to be able to afford the car, assuming the loan is for 60 months?

a) 5%
b) 6%
c) 7%
d) 8%

Answer 1

Jojuan would need an interest rate of 5% to be able to afford the car.

Step-by-step explanation:

To find the interest rate Jojuan would need to be able to afford the car, we can use the formula for the present value of an annuity:

PV = P imes rac{1 - (1 + r)^{-n}}{r}

Where PV is the present value (the cost of the car), P is the monthly payment, r is the interest rate (in decimal form), and n is the number of months. Rearranging the formula to solve for r:

rac{PV imes r}{P} = 1 - (1 + r)^{-n}

(1 + r)^{-n} = 1 - rac{PV imes r}{P}

By trial and error, we can find that a monthly interest rate of 5% would allow Jojuan to afford the car.