Mary buys a car whose total price is $23,499.

Question

She makes a down payment of $2000, and finances the rest as an auto loan at 3.35% compounded monthly. She will pay off the loan in equal amounts for five years. How much are the monthly payments? round your answe

Answer 1

Hi Alexis,

 

Our plan of attack will be as follows:

    1.  Find the Final Loan amount to be owed via the Compound Interest formula.

    2.  Divide the Final Loan amount by the number of months to get the Monthly Payment amount.

 

Let's begin by using the Compound Interest formula to find the Final Loan amount:

    F = P(1 + r/p)^(t)(p)  [Compound Interest formula]

         F (future amount) = unknown

         P (principal, i.e. initial amount) = 23,499 - 2000 = $21,499 (Total Price minus Down Payment)

         r (annual interest rate} = 3.35% = 3.35/100 = 0.0335

         p (number of periods in a year) = 12 (compounded monthly)

         t (years) = 5

    F = 21,499(1 + 0.0335/12)^(5)(12)

    F = 21,499(1 + 67/24000)⁶⁰

    F = 21,499(24067/24000)⁶⁰

    F = 21,499(1.182069401)

    F = 25,413.31005  [Final Loan amount]

 

Now, let's divide the Final Loan amount by the number of months to get the Monthly Payment amount:

    Monthly Payment amount = 25,413.31005 / (5)(12)

    Monthly Payment amount = 25,413.31005 / 60

    Monthly Payment amount = 423.5551675

    Monthly Payment amount = $423.56 (rounded to nearest penny)

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.