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18 December, 21:06

How much money should be deposited today in an account that earns 6% compounded semiannually so that it will accumulate to $14,000 in three years?

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  1. 18 December, 22:07
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    The amount of money to be deposited today is $11,725

    Step-by-step explanation:

    In this question, we are concerned with calculating the amount of money that should be deposited presently to have $14,000 in three years.

    To get this, we have to use the compound interest formula

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

    where A is the amount to be earned after the end of the compounding period which is $14,000 according to this question

    P is the initial amount to be deposited which is what we are looking for

    r is the rate of compounding which is 6% or simply 6/100 = 0.06

    n is the number of times interest is compounded yearly which is semiannually according to the question and this means 2

    t is the number of years which is 3 according to the question

    Now, plugging all these values, we have;

    14,000 = P (1 + 0.06/2) ^ (3 * 2)

    14,000 = P (1+0.03) ^6

    14,000 = P (1.03) ^6

    14,000 = 1.194P

    P = 14,000/1.194

    P = 11,724.77 which is approximately $11,725
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