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11 December, 17:36

Luke invests $4200 in an account that has an annual interest rate of 2.8% compounded semi-annually. Todd invests $3900 into an account that has an annual interest rate of 3.3% and is compounded continuously. After 8 years what is the difference between the two accounts?

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  1. 11 December, 18:09
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    Step-by-step explanation:

    Considering Luke's investment,

    Initial amount invested is $4200 This means that the principal is

    P = 4200

    It was compounded semi annually. This means that it was compounded twice in a year. So

    n = 2

    The rate at which the principal was compounded is 2.8%. So

    r = 2.8/100 = 0.028

    The investment was made for 8 years. So

    t = 8

    The formula for compound interest is

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

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

    A = 4200 (1+0.028/2) ^2 * 8

    A = 4200 (1.014) ^16 = $5246.34

    Considering Todd's investment,

    The formula for continuously compounded interest is

    A = P x e (r x t)

    where e is the mathematical constant approximated as 2.7183

    Therefore

    A = 3900 * 2.7183^ (0.033 * 8)

    A = 3900 * 2.7183^ (0.264)

    A = $5078.3

    The difference between the two accounts after 8 years would be

    5246.34 - 5078.3 = $168.04
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