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29 March, 16:58

Alex plans to invest $6000 for 10 years. Determine how much each investment would be worth to Alex as the CD matures.

A. Capitol Banks offers a 10 year CD at an annual rate of 5% using simple interest.

B. Charter Banks offers a 10 year CD at annual rate of 4.9% using monthly compound interest.

C. State Bank offers a 10 year CD at an annual rate of 4.8 % using continuous compounding.

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  1. 29 March, 18:01
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    Step-by-step explanation:

    A. The formula for determining simple interest is expressed as

    I = PRT/100

    Where

    I represents interest paid on the amount of money deposited.

    P represents the principal or amount of money deposited.

    R represents interest rate on the deposit.

    T represents the duration of the deposit in years.

    From the information given,

    P = $6000

    R = 5%

    T = 10 years

    Therefore,

    I = (6000 * 5 * 10) / 100

    I = $3000

    Total amount = 6000 + 3000 = $9000

    B. 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 = 6000

    r = 4.9% = 4.9/100 = 0.049

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

    t = 10 years

    Therefore,

    A = 6000 (1 + 0.049/12) ^12 * 10

    A = 6000 (1 + 0.049/12) ^120

    A = $9780

    C. The formula for continuously compounded interest is

    A = P x e^ (r x t)

    Where

    A represents the future value of the investment after t years.

    P represents the present value or initial amount invested

    r represents the interest rate

    t represents the time in years for which the investment was made.

    r = 4.8% = 4.8/100 = 0.048

    Therefore,

    A = 6000 x e^ (0.048 x 10)

    A = 6000 x e^ (0.48)

    A = $9696
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