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Lou Ling, owner of Lou's Lube, estimates that he will need $70,000 for new equipment in 7 years. Lou decided to put aside money today so it will be available in 7 years. Reel Bank offers Lou 6% interest compounded quarterly. How much must Lou invest to have $70,000 in 7 years?

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  1. Today, 02:20
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    The principal amount to be to be invested=$46,613.95

    Explanation:

    The total amount that Lou needs to invest with Reel bank in order to have for new equipment in 7 years is known as the principal amount.

    The formula for calculating total amount on investment compounded quarterly;

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

    A = the future value of the investment, including the interest

    P = the initial investment amount

    r = the annual interest rate

    n = the number of times that interest is compounded per unit t

    t = the time the money is invested or borrowed for

    For our case;

    A=$70,000

    P=p

    r=6/100=0.06

    n=compounded quarterly=4

    t=7 years

    replacing;

    70,000=p (1+0.06/4) ^ (4*7)

    70,000=p (1.015) ^28

    70,000=1.517 p

    1.517 p=70,000

    p=70,000/1.517

    p=46,613.95

    The principal amount to be to be invested=$46,613.95
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