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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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Answer:

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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