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2 April, 02:48

Carmen is acing for a new car that costs $15,000. If she puts $5000 in an account that earns 6% compounded monthly, how long will it take her to save enough money to buy the car?

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Answers (2)
  1. 2 April, 03:11
    0
    6 year
  2. 2 April, 04:16
    0
    Answer: it will take 18 years

    Step-by-step explanation:

    We would apply the formula for determining compound interest which is expressed as

    A = P (1+r/n) ^nt

    Where

    A = total amount in the account at the end of t years

    r represents the interest rate.

    n represents the periodic interval at which it was compounded.

    P represents the principal or initial amount deposited

    From the information given,

    P = 5000

    A = 15000

    r = 6% = 6/100 = 0.06

    n = 12 because it was compounded 12 times in a year.

    Therefore,.

    15000 = 5000 (1+0.06/12) ^12 * t

    15000/5000 = (1.005) ^12t

    3 = (1.005) ^12t

    Taking the log of both sides,

    Log 3 = log (1.005) ^12t

    0.4771 = 12t log1.005 = 12t * 0.0022

    0.0264t = 0.4771

    t = 0.4771/0.0264t

    t = 18
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