Olivia purchased a car worth $18,000 in the year 2001. It loses its value by 6% per year. What is the value of the car in 2004? Round to the nearest cent.

The value of car in 2004 is $14951, if Olivia purchased a car worth $18,000 in the year 2001 and it loses its value by 6% per year.

Step-by-step explanation:

The given is,

                Car worth $18,000 in the year 2001

                Loses its value by 6% per year

Step:1

              Formula to calculate the worth of car with loss rate,

                                     .....................................(1)

             Where,   y = Value of car after t period

                            A = Initial value of car

                             r = Loss rate

                             t = Time period

             From give,

                          A = $18,000

                           r = 6 % per year

                           t = 3 years

             Equation (1) becomes,

                                      = (18000 × 0.830584)

                                      = 14950.512

                                      ≅ 14951

             Value of car in 2004, y = $14951

                                    ( or )

Step:1

             t = 3 years                                    ( 2001 to 2004 )

            For 1st year,

                          = ( Worth of car in previous year ) -

                                      ( Worth of car in previous year × Loss rate )

                         = ( 18000 ) - ( 18000 × 0.06 )

                         = 18000 - 1080

                         = $16920

             For 2nd year,

                         = ( 16920 ) - ( 16920 × 0.06 )

                         = 16920 -1015.2

                         = $15904.8

             For 3rd year,

                         = ( 15904.8 ) - ( 15904.8 × 0.06 )

                         = 15904.8 - 954.288

                         = 14950.512

                        ≅ $14951

Result:

           The value of car in 2004 is $14951, if Olivia purchased a car worth $18,000 in the year 2001 and it loses its value by 6% per year.  

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