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7 October, 03:43

Alfredo has two offers for his grocery shop. The first offer is a cash payment of $60,000, and the second is a down payment of $10,000 with payments of $6,000 at the end of each semiannual period for 5 years. Assuming an interest rate of 6% compounded semiannually, find the difference between the two present values. State the answer as an absolute value.

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  1. 7 October, 05:55
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    First Offer

    Present value = $60,000

    Second Offer

    PV = Down payment + A (1 - (1 + r/m) - nm

    r/m

    PV = $10,000 + $6,000 (1 - (1 + 0.06/2)) - 5x2

    0.06/2

    PV = $10,000 + $6,000 (1 - (1 + 0.03)) - 10

    0.03

    PV = $10,000 + 6,000 (1 - (1.03)) - 10

    0.03

    PV = $10,000 + 6,000 (8.5302)

    PV = $61,181

    The difference between the two present values

    = $61,181 - $60,000

    = $1,181

    Explanation:

    The present value of the cash payment is $60,000. The present value of the second offer is the down payment plus the present value of semi-annual payments. We need to use the present value of annuity formula so as to determine the present value of semi-annual payments. Then. we will deduct the present value of the first offer from the present value of the second offer in order to obtain difference in present values.
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