The price of a new car is $24,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 10%/year compounded monthly. (Round your answers to the nearest cent.)

Question

(a) What monthly payment will she be required to make if the car is financed over a period of 36 months? Over a period of 48 months?

(b) What will the interest charges be if she elects the 36-month plan? The 48-month plan?

I do not know where to start, or what to do with the 25% in the formula?

Answer 1

The 25% means that she pays up front $6000 so she only needs to finance $18000.
Over a period of 36 months,
n=36=periods of one month
i, monthly interest = 0.1/12
P, principal = 18000
R=rate=1+i=1+1/120
Monthly payment, A
=PRⁿ(R-1)/(Rⁿ-1)
=18000*(1+1/120)³⁶*(1/120)/((1+1/120)³⁶-1)
=$580.81

Similarly, for 48-month loan,
Monthly payment, A
=PRⁿ(R-1)/(Rⁿ-1)
=18000*(1+1/120)⁴⁸*(1/120)/((1+1/120)⁴⁸-1)
=$456.53

For interest charges, subtract $18000 from the product of monthly payment multiplied by the number of payments.