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5 May, 13:13

A new tax business, Taxes Done Right, will purchase a copying machine. After speaking with their financial advisor, they find that the copying machine will cost them $3,300 in 3 years. The account they will invest in earns 5% per year compounded semi-annually. In order to pay cash for the machine, how much should they deposit semi-annually in this account for 3 years?

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  1. 5 May, 14:04
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    Answer: $2,845.57965

    The principal to be deposited semiannually would be $2,845.58 (rounded to 2 decimal places)

    Explanation:

    Using compound formula below

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

    A = amount = $3,300

    r = rate = 5% = 5/100 = 0.05

    n = number of compounding rate (semiannually) = 2 interest payments a year

    t = time in years = 3

    3,300 = p (1 + 0.05/2) ^2 (3)

    3,300 = p (1 + 0.025) ^6

    3,300 = p (1.025) ^6

    3,300 = 1.15969342p

    Divide both sided by 1.15969342

    p = $ (3,300/1.15969342)

    p = $2,845.57965

    p ≈$2,845.58 rounded to 2 decimal places.
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