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13 August, 17:05

McDonald's major distribution partner, The Martin-Brower Company, needs at least $1 million to build a new warehouse in Medicine Hat two years from today. To date, it has invested $500,000. If it continues to invest $50,000 at the end of every quarter into a fund earning 6% quarterly, will it have enough money to build the warehouse two years from now? Show calculations to support your answer

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  1. 13 August, 17:25
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    No it wont have enough money to build a warehouse in two years.

    Explanation:

    Firstly we are given that the warehouse is $1 million so the company needs to save this amount of money in two years time.

    We know that the company has invested $500000 to date therefore we need to calculate if this $50000 per quarter investment will cover the the other portion for $500000 to meet the warehouse cost of $1 million so we will use the future value annuity formula to calculate this which is:

    Fv = C[ ((1+i) ^n - 1) / i]

    where Fv will be the future value after two years of the $50000 investment

    C is the periodic payment of $50000

    i is the interest rate per period which is 6% per quarter

    n is the number of periods the payment is done here it is 4 x 2years = 8 periods / investments of $50000 that will be done.

    thereafter we substitute on the above formula:

    Fv = 50000[ ((1+6%) ^8 - 1) / 6%]

    Fv = $494873.40

    then we combine this amount to $500000 to see if it reaches $1 million

    $494873.40 + $500000 = $994873.40 which is close to the warehouse cost of $1 million but it does not reach it so the company wont have enough money to purchase the warehouse.
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