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23 February, 03:17

If you invest in P dollars and you want the investment to grow to A dollars in t years, the interest rate that must be earned if interest is compounded annually is given by the formula

r = t√A/P-1

If you invest $4000 and want to have $8500 in 8 years, what interest rate must be earned? Round to at least 1 decimal place.

You need an interest rate of at least percent.

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  1. 23 February, 03:42
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    Answer: You need an interest rate of at least 9.9%

    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,

    A = $8500

    P = $4000

    n = 1 because it was compounded once in a year.

    t = 8 years

    Therefore,

    8500 = 4000 (1 + r/1) ^1 * 8

    8500/4000 = (1 + r) ^8

    2.125 = (1 + r) ^8

    Taking log of both sides of the equation, it becomes

    Log 2.125 = 8 log (1 + r)

    0.327 = 8 log (1 + r)

    0.327/8 = 8 log (1 + r)

    0.040875 = log (1 + r)

    Taking inverse log of both sides of the equation, it becomes

    10^0.040875 = 10^log (1 + r)

    1.099 = 1 + r

    r = 1.099 - 1

    r = 0.099

    r = 0.099 * 100 = 9.9%
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