The first table gives the present value of $1 at the end of different time perio
ID: 2801791 • Letter: T
Question
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 Periods
Table 13.4 Present Value of $1 to Be Received at the End of Each Period for a Given Number of Periods
QUESTION: 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 $20,000 per year more, over the next 50 years, than it would have been had he not attended college. Should he go to college? Assume that each payment for college and dollar of income earned occur at the end of the years in which they occur. Ignore possible income taxes in making your calculations. Decide whether you should attend college, assuming each of the following interest rates:
A) 2%
B) 4%
C) 6%
D) 8%
Percent Interest Period 2 4 6 8 10 12 14 16 18 20 1 0.980 0.962 0.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 2 0.961 0.925 0.890 0.857 0.826 0.797 0.769 0.743 0.718 0.694 3 0.942 0.889 0.840 0.794 0.751 0.712 0.675 0.641 0.609 0.579 4 0.924 0.855 0.792 0.735 0.683 0.636 0.592 0.552 0.515 0.442 5 0.906 0.822 0.747 0.681 0.621 0.567 0.519 0.476 0.437 0.402 10 0.820 0.676 0.558 0.463 0.386 0.322 0.270 0.227 0.191 0.162 15 0.743 0.555 0.417 0.315 0.239 0.183 0.140 0.180 0.084 0.065 20 0.673 0.456 0.312 0.215 0.149 0.104 0.073 0.051 0.037 0.026 25 0.610 0.375 0.233 0.146 0.092 0.059 0.038 0.024 0.016 0.010 40 0.453 0.208 0.097 0.046 0.022 0.011 0.005 0.003 0.001 0.001 50 0.372 0.141 0.054 0.021 0.009 0.003 0.001 0.001 0 0Explanation / Answer
(A) At 2 % interest rate the present value of a stream of 1$ paid/recieved for 4 years is $3.808 and paid/received for 50 years is $31.424. The present value of $1 to be paid 4 years from now at 2% is $0.924
Net Outflow and Loss of Cash Flow ( per year) = College Fees + Loss in Potential Income = 10000 + 25000 = $ 35000
Therefore, the PV of $ 35000 for four years at 2 % = 35000 x 3.808 = $ 133280 (1)
The PV of Future Income for 50 years at 2 % after four years = 20000 x 31.424 = $ 628480 (this is PV of future incomes at t=4 years and not today)
Therefore, PV of Future Income for 50 years at 2 % today = 628480 x 0.924 = $ 577352.16 (2)
Net Present Value = (2) - (1) = 577352.16 - 133280 = $ 444072.16
Since , Net Present Value is positive Mark Jones Should attend college.
(B) At 4 % interest rate the present value of a stream of 1$ paid/recieved for 4 years is $3.630 and paid/received for 50 years is $21.482. The present value of $1 to be paid 4 years from now at 4% is $0.855
Net Outflow and Loss of Cash Flow ( per year) = College Fees + Loss in Potential Income = 10000 + 25000 = $ 35000
Therefore, the PV of $ 35000 for four years at 4 % = 35000 x 3.630 = $ 127050 (1)
The PV of Future Income for 50 years at 4 % after four years = 20000 x 21.482 = $ 429640 (this is PV of future incomes at t=4 years and not today)
Therefore, PV of Future Income for 50 years at 2 % today = 429640 x 0.855 = $ 367342.2 (2)
Net Present Value = (2) - (1) = 367342.2 - 127050 = $ 240292.2
Since , Net Present Value is positive Mark Jones Should attend college.
(C) At 6% interest rate the present value of a stream of 1$ paid/recieved for 4 years is $3.465 and paid/received for 50 years is $15.762. The present value of $1 to be paid 4 years from now at 6% is $0.792
Net Outflow and Loss of Cash Flow ( per year) = College Fees + Loss in Potential Income = 10000 + 25000 = $ 35000
Therefore, the PV of $ 35000 for four years at 6% = 35000 x 3.465 = $ 121275 (1)
The PV of Future Income for 50 years at 6% after four years = 20000 x 15.762 = $ 315240 (this is PV of future incomes at t=4 years and not today)
Therefore, PV of Future Income for 50 years at 6% today = 315240 x 0.792 = $ 249670.08 (2)
Net Present Value = (2) - (1) = 249670.08 - 121275 = $ 128395.08
Since , Net Present Value is positive Mark Jones should attend college.
(D) At 8% interest rate the present value of a stream of 1$ paid/recieved for 4 years is $3.312 and paid/received for 50 years is $12.233. The present value of $1 to be paid 4 years from now at 8% is $0.735
Net Outflow and Loss of Cash Flow ( per year) = College Fees + Loss in Potential Income = 10000 + 25000 = $ 35000
Therefore, the PV of $ 35000 for four years at 8% = 35000 x 3.312 = $ 115920 (1)
The PV of Future Income for 50 years at 8% after four years = 20000 x 12.233 = $ 244660 (this is PV of future incomes at t=4 years and not today)
Therefore, PV of Future Income for 50 years at 8% today = 244640 x 0.735 = $ 179825.1 (2)
Net Present Value = (2) - (1) = 179825.1 - 115920 = $ 63905.1
Since , Net Present Value is positive Mark Jones Should attend college.
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