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4 May, 08:33

To save for a new car, Trafton invested $7,000 in a savings account that earns 6.5% interest, compounded continuously. After four years, he wants to buy a used car for $10,000. How much money will he need to pay in addition to what is in his savings account? (Round your answer to the nearest cent.)

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  1. 4 May, 11:09
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    Trafton will need to pay $ 900 in addition to what is in his savings account, to buy the used car he wants.

    Step-by-step explanation:

    1. Let's review the information given to us to answer the question correctly:

    Initial deposit = $ 7,000

    Annual interest = 6.5% = 0.065 compounded continuously

    Time of the investment = 4 years

    Price of the used car Trafton wants to buy = $ 10,000

    2. How much money will he need to pay in addition to what is in his savings account?

    1. For answering the question, let's calculate how much money Trafton has in his savings account after 4 years, this way:

    FV = PV * e ^ (i * t)

    Where,

    FV = Future value of the initial deposit after t time

    PV = Initial deposit

    e = Euler's number (2.7183)

    i = 0.065 compounded continuously

    t = 4 years

    Replacing with the real values, we have:

    FV = 7,000 * 2.7183^ (0.065 * 4)

    FV = 7,000 * 1.30 (Rounding to the nearest hundredth)

    FV = $ 9,100

    Now, we can elaborate how much money will Trafton need to pay in addition, as follows:

    Money in addition = Price of the used car Trafton wants to buy - Future Value of the savings account after 4 years

    Money in addition = 10,000 - 9,100

    Money in addition = $ 900

    Trafton will need to pay $ 900 in addition to what is in his savings account, to buy the used car he wants.
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