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1 March, 08:13

Carlene is saving her money to buy a $500 desk. She deposits $400 into an account with an annual interest rate of 6% compounded continuously. The equation represents the situation, where t is the number of years the money needs to remain in the account. About how long must Carlene wait to have enough money to buy the desk? Use a calculator and round your answer to the nearest whole number.

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  1. 1 March, 08:18
    0
    Carlene is saving her money to buy a $500 desk. She deposits $400 into an account with an annual interest rate of 6% compounded continuously.

    The equation represents the situation, where t is the number of years the money needs to remain in the account.

    About how long must Carlene wait to have enough money to buy the desk? Use a calculator and round your answer to the nearest whole number.

    Formula for Compound Interest A = ((P * (1+i) ^n)

    Where

    A = final amount

    P = initial principal balance

    r = interest rate

    n = number of times interest applied per time period

    t = number of time periods elapsed

    500 = ((400 * (1+0.06) ^n)

    500 = 400 * 1.06) ^n

    Divide both sides by 400

    1.25 = 1.06^n

    n = log 1.06 x 1.25 = 0.0312

    Converted to months = 0.0312 * 12 months = 11 days
  2. 1 March, 08:22
    0
    Answer: Carlene must wait 4 years.
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