Business, 10.09.2019 05:30, lexident

Auniversity of iowa basketball standout is offered a choice of contracts by the new york liberty.
the first one gives her $100,000 one year from today and $100,000 two years from today. the second
one gives her $132,000 one year from today and $66,000 two years from today. as her agent, you must
compute the present value of each contract. which of the following interest rates is the lowest one at
which the present value of the second contract exceeds that of the first?
a. 7 percent
b. 8 percent
c. 9 percent
d. 10 percent
a. 7 percent

Answers: 3

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Answers

answered: cuddleslugsovifat

The lowest interest rate at which the present value of the second contract exceeds that of the first is a. 7 percent.

Explanation:

Calculating present values is a useful way to compare cases where money is to be received in the future. The higher the present value (when comparing cases where you get money), the better. To calculate it, we make use of the next formula:

$PV=\frac{C}{(1+r)^{n}}$

Where PV: Present value,

C: Cash flow at a given period,

r: Interest rate, and

n: Number of periods that will have passed (in this case, we are talking about years).

Now, since we are getting money twice in each case (the first payment one year from today, and the final payment two years from today), we can restructure our present value formula to include these two payments. We will get something like this:

$PV=\frac{C_1}{1+r}+\frac{C_2}{(1+r)^{2}}$

Notice how each fraction represents one of the payments received, with one having an 'n' of 1 year, and the other one having an 'n' of 2 years. C₁ and C₂ represent the first and the second payment, respectively.

Now that we have our completed formula, let's review each contract's present value (PV) with the lowest interest rate (7%), just to see how it turns out. Remember that 7% equals 0.07 in any formula:

Contract A) This one gives her $100,000 one year from today and $100,000 two years from today.

$PV_{A,0.07}=\frac{100000}{1+0.07}+\frac{100000}{(1+0.07)^{2}}\\PV_{A,0.07}=93457.944+87343.873\\PV_{A,0.07}=180801.817dollars$

So Contract A's present value at 7% interest rate would be equal to $180801.817.

Contract B) The second one gives her $132,000 one year from today and $66,000 two years from today.

$PV_{B,0.07}=\frac{132000}{1+0.07}+\frac{66000}{(1+0.07)^{2}}\\PV_{B,0.07}=123364.486+57646.956\\PV_{B,0.07}=181011.442dollars$

So Contract B's present value at 7% interest rate would be equal to $181011.442, which exceeds that of Contract A.

Since among our options of interest rates, 7 percent is the lowest one, and, with this taken into account, the present value of the second contract (Contract B) exceeded that of the first (Contract A), the answer is a. 7 percent.

answered: Guest

whole quiz

1. the sum of all activities involved in getting high-quality products into the marketplace

2.operations

3. the principle of looking at the supply chain as a whole in order to improve the overall flow through the system.

4. produced; performed

5. activities producing tangible products, such as radios, newspapers, buses, and textbooks.

6. activities producing intangible and tangible products, such as entertainment, transportation, and education.

7. customer focus

8. analyzing a competitor's products to identify desirable improvements

9. the systematic direction and control of the processes that transform resources into finished projects that create value for and provide benefits to consumers.

10. operation management.

your welcome leave a rate and a < 3

answered: Guest

answer; niosh, the national institute for occupational safety and health;

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Auniversity of iowa basketball standout is offered a choice of contracts by the new york liberty.