The price of a car is currently 120,000$. The price of the car decreases annually by 2.5%. What is the price of the car after 8 years?

Question

The price of a car is currently 120,000$. The price of the car decreases annually by 2.5%. What is the price of the car after 8 years?

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Sapo 3 years 2021-09-03T08:27:24+00:00 2 Answers 3 views 0

Answers ( )

  1. kiet
    0
    2021-09-03T08:28:46+00:00
    Reply

    oh I did a mistake earlier , pardon ^^”

    • Current price (Pₒ) = 120, 000 $
    • Rate of Depreciation (R) = 2. 5%
    • Total Time = 8 years

    Let price after 8 years be P.

    Using the compound interest formula of shrinking principal :-

    P = Pₒ( 1 – R/ 100) ᵀ

    P = 120, 000 ( 1 – 2.5/ 100)ᵀ

    P = 120, 000 { (100 – 2.5)/ 100}ᵀ

    P = 120, 000{ 97. 5/ 100 }ᵀ

    P = 120, 000 {0. 975 } ⁸

    P = 120, 000 { 0. 8166}

    P = 97,998.216 $

    Since, P is is price after 8 years

    Answer:-

    The price of the car after 8 years will be 97, 998. 216 $

  2. thuthuy
    0
    2021-09-03T08:29:07+00:00
    Reply

    Answer:

    97,988.216

    Step-by-step explanation:

    So, we can find this by using the following formula:

    First value(change)^time

    We know that the orginal, or first value, is 120,000.

    We know that the time interval for this is 8 years, which is our time value.

    We know that the decrease in this price is 2.5%. However, this is not our change.

    Our change is the 97.5% price that is left.

    This makes sense, because you would get a super small price when you use 2.5% as change.

    So to sum up what we have done so far:

    First value – 120,000

    Change – 100%-2.5% = 97.5%. In decimal form: 0.975

    Time – 8

    So lets plug these into:

    First_.value(change)^t^i^m^e

    =

    120,000(0.975)^8

    And remember your order of operations here.

    We dont have any equations or expressions inside the parethese, so we can move on to what comes next – exponents.

    We have the exponent 8, which is attached to the 0.975.

    So in your calculator, take 0.975, and put it to the 8th power.

    You should get 0.816651803662261962890625

    Lets leave it like this, becuase 120,000 is a very large value, and rounding what you multiply could change what you get in the end.

    Now  our equation looks like:

    120,000(0.816651803662261962890625)

    We have done parethese, exponents – now we have multiplication and division.

    We do indeed have this, since 120,000(0.816651803662261962890625) could also be written as:

    120,000*0.816651803662261962890625

    Now multiplying this you should get:

    97,998.216439471435546875

    This is where you can round your answer.

    I do not know what exactly they want you to round to, so its safe to just round your answer to the hundreths place:

    97,998.22

    So this is the new price of the car!

    Hope this helps!

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