4 pages/≈1100 words
Mathematics & Economics
Risk and Uncertainty in Economics (Math Problem Sample)
Risk and uncertainty in economics
Risk and uncertainty in economics
The value of the second alternative is analyzed below:
The formula for finding the present value based on the future is provided by
The Future Amountâ€™s PV=A(1+r)n
A represents the amount of annuity while r is the opportunity rate of interest and in the period of years when the amount was received. Basing on this fomularae, the present value of the second alternative can be found by adding the future amount of the two years.
Therefore, present value=
700000(1+0.08)1 + 700000(1+0.08)2 = $(6, 481,481.48+6,001,371.74)
$ 12, 482, 853.22
Since the amount provided in one lump sum was only12 million, the second alternative appears to be the best option since it avails students with 12.482 million dollars which is 0.482 more that the lump sum provided in the initial scholarship.
Since the new opportunity rate of interest is 12 percent, the calculation will be modified so as to show the variance of the newly provided parameter.
Therefore, the second alternative can be calculated by
700000(1+0.12)1 + 700000(1+0.12)2 = $(6, 250, 000 + 5,580,357.14)
=11.83 million dollars.
Since the amount provided in one lump sum is 12 million dollars, it appear best suit in this new situation as the second option provides 11.83 million dollars that are $ 170, 000 less than the initial option.
In a real world setting, managers in financial institutions utilize Present Value (NPV/FPV) scales to examine the time value of money (NPV). For instance, availing a service in one year then receiving payment a year later. In such situation, the company provides a service in January 2015 and agrees to pay 100 dollars in January 2016. The time of money will assist the financial manager to understand that component of $ 100 is interest, which is for waiting one year for $ 100. Maybe only $ 80 of the $ 100 is the earned serviced revenue in 2015, and the $ 20 interest will be earned in 2016. When calculating the present value, the managers will eliminate the interest so as to calculate the service revenue. One more real life scenario is dealing with land. The owner of the land may opt to sell it for $120,000 if the money is received today, or opt to be paid $250,000 after one year. At the end of the year, he would earn much more than he would decide to sell the farm today.
Cash for year1 = (0.2Ã—50) + (0.1Ã—20) + (0.4Ã—30) + (0.3Ã—40) = $36 ...
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