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13 May, 04:47

A couple needs $55,000 as a down payment for a home. If they invest the $40,000 they have at 12% compounded quarterly, how long will it take for the money to grow to $55,000

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  1. 13 May, 08:38
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    approximately 2.7 years

    Explanation:

    The formula for calculating Compound Interest is

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

    Where P = principal amount (the initial amount you borrow or deposit)

    r = annual rate of interest (as a decimal)

    t = number of years the amount is deposited or borrowed for.

    A = amount of money accumulated after n years, including interest.

    n = number of times the interest is compounded per year

    A = $55,000

    P = $40,000

    r = 12% = 0.12

    n = 4

    We are to look for t = number of years the amount is deposited or borrowed for

    55,000 = 40,000 (1 + 0.12/4) ^4t

    55,000 = 40,000 (1.03) ^4t

    55,000/40,000 = 1.03^4t

    1.375 = 1.03^4t

    1.03^10.77 = 1.03^4t

    4t = 10.77

    t = 10.77/4

    t = 2.7 years
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