The owner of a residential building lot has received two purchases offers.Mrs A is offering a $20,000 downpayment plus $40,000 payable in one year.Mr B's offer is $15,000 downlayment plus two $25,000 payment due one and two years from now.Which offer has teh great economic value if money can earn 3.5% compounding quarterly?how much more is it worth in current dollars?
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As for the question itself, it is incomplete. How can anyone tell what the building is worth in current dollars if we don't know when it was sold at the price bid in the first part of the question?
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To determine which offer has the greater economic value, we need to compare the present values of the two offers.
Let's start by calculating the present value of Mrs A's offer, which includes a $20,000 downpayment plus $40,000 payable in one year.
Step 1: Calculate the present value of the $20,000 downpayment:
To determine the present value of a future payment, we need to discount it based on the given interest rate and compounding period.
PV = FV / (1 + r/n)^(n*t)
Where:
PV = Present Value
FV = Future Value
r = Interest rate (in decimal form)
n = Compounding periods per year
t = Number of years
Using the formula, let's calculate the present value of the $20,000 downpayment:
PV1 = $20,000 / (1 + 0.035/4)^(4*1)
= $20,000 / (1 + 0.00875)^(4)
= $20,000 / (1.00875)^(4)
= $20,000 / 1.03420
≈ $19,337.23
So, the present value of Mrs A's downpayment is approximately $19,337.23.
Step 2: Calculate the present value of the $40,000 payable in one year:
Similarly, we can calculate the present value of the $40,000 payment due in one year:
PV2 = $40,000 / (1 + 0.035/4)^(4*1)
= $40,000 / (1.00875)^(4)
≈ $38,674.46
Therefore, the present value of Mrs A's offer is approximately $19,337.23 + $38,674.46 = $58,011.69.
Now let's calculate the present value of Mr B's offer, which includes a $15,000 downpayment plus two $25,000 payments due one and two years from now.
Step 1: Calculate the present value of the $15,000 downpayment:
Using the same formula:
PV3 = $15,000 / (1 + 0.035/4)^(4*1)
= $15,000 / (1.00875)^(4)
≈ $14,502.92
Step 2: Calculate the present value of the two $25,000 payments due in one and two years:
To calculate the present value of multiple cash flows, we need to calculate the present value of each cash flow separately and then sum them up.
PV4 = $25,000 / (1 + 0.035/4)^(4*1)
≈ $24,131.76
PV5 = $25,000 / (1 + 0.035/4)^(4*2)
≈ $23,351.92
Therefore, the total present value of Mr B's offer is approximately $14,502.92 + $24,131.76 + $23,351.92 = $62,986.61.
To determine which offer has the greater economic value, we compare the present values:
Mrs A's offer: $58,011.69
Mr B's offer: $62,986.61
Mr B's offer has the greater economic value.
To calculate how much more Mr B's offer is worth in current dollars, subtract the present value of Mrs A's offer from the present value of Mr B's offer:
$62,986.61 - $58,011.69 = $4,974.92
Therefore, Mr B's offer is worth approximately $4,974.92 more in current dollars.