The charging of interest rates is often viewed with contempt.
1)The charging of interest rates is often viewed with contempt. Do interest rates serve any useful purpose?2)How does an increase in interest rates affect the present value of a future payment?3)How does an increase in the size of a future payment affect the present value of the future payment?4)Two payments of $1,000 are to be made. One of them will be paid one year from today and the other will be paid two years from today. Which has the greater present value? Why?Use the tables below to answer Problems 1â3 The first table gives the present value of $1 at the end of different time periods, given different interest rates. For example, at an interest rate of 10%, the present value of $1 to be paid in 20 years is $0.149. At 10% interest, the present value of $1,000 to be paid in 20 years equals $1,000 times 0.149, or $149. The second table gives the present value of a stream of payments of $1 to be made at the end of each period for a given number of periods. For example, at 10% interest, the present value of a series of $1 payments, made at the end of each year for the next 10 years, is $6.145. Using that same interest rate, the present value of a series of 10 payments of $1,000 each is $1,000 times 6.145, or $6,145.Table 13.3 Present Value of $1 to Be Received at the End of a Given Number of PeriodsPercent InterestPeriod246810121416182010.9800.9620.9430.9260.9090.8930.8770.8620.8470.83320.9610.9250.8900.8570.8260.7970.7690.7430.7180.69430.9420.8890.8400.7940.7510.7120.6750.6410.6090.57940.9240.8550.7920.7350.6830.6360.5920.5520.5150.44250.9060.8220.7470.6810.6210.5670.5190.4760.4370.402100.8200.6760.5580.4630.3860.3220.2700.2270.1910.162150.7430.5550.4170.3150.2390.1830.1400.1800.0840.065200.6730.4560.3120.2150.1490.1040.0730.0510.0370.026250.6100.3750.2330.1460.0920.0590.0380.0240.0160.010400.4530.2080.0970.0460.0220.0110.0050.0030.0010.001500.3720.1410.0540.0210.0090.0030.0010.00100Table 13.4 Present Value of $1 to Be Received at the End of Each Period for a Given Number of PeriodsPercent InterestPeriod246810121416182010.9800.9620.9430.9260.9090.8930.8770.8620.8470.83321.9421.8861.8331.7831.7361.6901.6471.6051.5661.52832.8842.7752.6732.5772.4872.4022.3222.2462.1742.10643.8083.6303.4653.3123.1703.0372.9102.7982.6902.58954.7134.4524.2123.9933.7913.6053.4333.2743.1272.991108.9838.1117.3606.7106.1455.6505.2164.8334.4944.1921512.84911.7189.7128.5597.6066.8116.1425.5755.0924.6752016.35113.59011.4709.8188.5147.4696.6235.9295.3534.8702519.52315.62212.78310.6759.0777.8436.8736.0975.4674.9483022.39617.29213.76511.2589.4278.0557.0036.1775.5174.9794027.35519.79315.04611.9259.7798.2447.1056.2335.5484.9975031.42421.48215.76212.2339.9158.3047.1336.2465.5544.9991)Your Uncle Arthur, not to be outdone by Aunt Carmen, offers you a choice. You can have $10,000 now or $30,000 in 15 years. If you took the payment now, you could put it in a bond fund or bank account earning 8% interest. Use present value analysis to determine which alternative is better.2)Remember Carol Steinâs tractor? We saw that at an interest rate of 7%, a decision to purchase the tractor would pay off; its net present value is positive. Suppose the tractor is still expected to yield $20,000 in net revenue per year for each of the next 5 years and to sell at the end of 5 years for $22,000; and the purchase price of the tractor still equals $95,000. Use Tables (a) and (b) to compute the net present value of the tractor at an interest rate of 8%.3)Mark Jones is thinking about going to college. If he goes, he will earn nothing for the next four years and, in addition, will have to pay tuition and fees totaling $10,000 per year. He also would not earn the $25,000 per year he could make by working full time during the next four years. After his four years of college, he expects that his income, both while working and in retirement, will be $20,000 per year more, over the next 50 years, than it would have been had he not attended college. Should he go to college? Assume that each payment for college and dollar of income earned occur at the end of the years in which they occur. Ignore possible income taxes in making your calculations. Decide whether you should attend college, assuming each of the following interest rates:3A) 2%3B) 4%3C) 6%3D) 8%
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