Finite Math

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.)

(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?

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  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.

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