Part CThis Table Was Used To Calculate The Present Value Of Each Payment Earlier In The Lesson, With A Total Of $878,611. How Does Your Answer From Part B Compare To The Total Calculated From The Table? [ \begin{tabular}{|c|c|c|} \hline &
Introduction
In the previous sections, we explored the concept of present value and its application in financial calculations. We used a table to calculate the present value of each payment, resulting in a total of $878,611. In this section, we will compare our answer from part B with the total calculated from the table. This analysis will provide valuable insights into the accuracy of our calculations and the reliability of the table.
Understanding the Table
The table used to calculate the present value of each payment is a crucial component of our analysis. It provides a clear and concise representation of the present value of each payment, allowing us to easily compare our calculations with the total calculated from the table.
| Year | Payment | Present Value |
|---|---|---|
| 1 | $100,000 | $90,909 |
| 2 | $120,000 | $108,108 |
| 3 | $150,000 | $135,135 |
| 4 | $180,000 | $162,162 |
| 5 | $200,000 | $180,180 |
| 6 | $220,000 | $198,198 |
| 7 | $250,000 | $225,225 |
| 8 | $280,000 | $252,252 |
| 9 | $300,000 | $270,270 |
| 10 | $320,000 | $288,288 |
| 11 | $350,000 | $315,315 |
| 12 | $380,000 | $342,342 |
| 13 | $400,000 | $360,360 |
| 14 | $420,000 | $378,378 |
| 15 | $450,000 | $405,405 |
| 16 | $480,000 | $432,432 |
| 17 | $500,000 | $450,450 |
| 18 | $520,000 | $468,468 |
| 19 | $550,000 | $495,495 |
| 20 | $580,000 | $522,522 |
| 21 | $600,000 | $540,540 |
| 22 | $630,000 | $558,558 |
| 23 | $660,000 | $576,576 |
| 24 | $690,000 | $594,594 |
| 25 | $720,000 | $612,612 |
| 26 | $750,000 | $630,630 |
| 27 | $780,000 | $648,648 |
| 28 | $810,000 | $666,666 |
| 29 | $840,000 | $684,684 |
| 30 | $870,000 | $702,702 |
| 31 | $900,000 | $720,720 |
| 32 | $930,000 | $738,738 |
| 33 | $960,000 | $756,756 |
| 34 | $990,000 | $774,774 |
| 35 | $1,020,000 | $792,792 |
| 36 | $1,050,000 | $810,810 |
| 37 | $1,080,000 | $828,828 |
| 38 | $1,110,000 | $846,846 |
| 39 | $1,140,000 | $864,864 |
| 40 | $1,170,000 | $882,882 |
| 41 | $1,200,000 | $900,900 |
| 42 | $1,230,000 | $918,918 |
| 43 | $1,260,000 | $936,936 |
| 44 | $1,290,000 | $954,954 |
| 45 | $1,320,000 | $972,972 |
| 46 | $1,350,000 | $990,990 |
| 47 | $1,380,000 | $1,008,008 |
| 48 | $1,410,000 | $1,025,025 |
| 49 | $1,440,000 | $1,042,042 |
| 50 | $1,470,000 | $1,059,059 |
| 51 | $1,500,000 | $1,076,076 |
| 52 | $1,530,000 | $1,093,093 |
| 53 | $1,560,000 | $1,110,110 |
| 54 | $1,590,000 | $1,127,127 |
| 55 | $1,620,000 | $1,144,144 |
| 56 | $1,650,000 | $1,161,161 |
| 57 | $1,680,000 | $1,178,178 |
| 58 | $1,710,000 | $1,195,195 |
| 59 | $1,740,000 | $1,212,212 |
| 60 | $1,770,000 | $1,229,229 |
| 61 | $1,800,000 | $1,246,246 |
| 62 | $1,830,000 | $1,263,263 |
| 63 | $1,860,000 | $1,280,280 |
| 64 | $1,890,000 | $1,297,297 |
| 65 | $1,920,000 | $1,314,314 |
| 66 | $1,950,000 | $1,331,331 |
| 67 | $1,980,000 | $1,348,348 |
| 68 | $2,010,000 | $1,365,365 |
| 69 | $2,040,000 | $1,382,382 |
| 70 | $2,070,000 | $1,399,399 |
| 71 | $2,100,000 | $1,416,416 |
| 72 | $2,130,000 | $1,433,433 |
| 73 | $2,160,000 | $1,450,450 |
| 74 | $2,190,000 | $1,467,467 |
| 75 | $2,220,000 | $1,484,484 |
| 76 | $2,250,000 | $1,501,501 |
| 77 | $2,280,000 | $1,518,518 |
| 78 | $2,310,000 | $1,535,535 |
| 79 | $2,340,000 | $1,552,552 |
| 80 | $2,370,000 | $1,569,569 |
| 81 | $2,400,000 | $1,586,586 |
| 82 | $2,430,000 | $1,603,603 |
| 83 | $2,460,000 | $1,620,620 |
| 84 | $2,490,000 | $1,637,637 |
| 85 | $2,520,000 | $1,654,654 |
| 86 | $2,550,000 | $1,671,671 |
| 87 | $2,580,000 | $1,688,688 |
| 88 | $2,610,000 | $1,705,705 |
| 89 | $2,640,000 | $1,722,722 |
| 90 | $2,670,000 | $1,739,739 |
| 91 | $2,700,000 | $1,756,756 |
| 92 | $2,730,000 | $1,773,773 |
| 93 | $2,760,000 | $1,790,790 |
| 94 | $2,790,000 | $1,807,807 |
| 95 | $2,820,000 | $1,824,824 |
| 96 | $2,850,000 | $1,841,841 |
| 97 | $2,880,000 | $1,858,858 |
| 98 | $2,910,000 | $1,875,875 |
| 99 | $2,940,000 | $1,892,892 |
| 100 | $2,970,000 | $1,909,909 |
| 101 | $3,000,000 | $1,926,926 |
| 102 | $3,030,000 | $1,943,943 |
| 103 | $3,060,000 | $1,960,960 |
| 104 | $3,090,000 | $1,977,977 |
| 105 | $3,120,000 | $1,995,995 |
| 106 | $3,150,000 | $2,013,013 |
| 107 | $3,180,000 | $2,030,030 |
| 108 | $3,210,000 | $2,047,047 |
| 109 | $3,240,000 | $2,064,064 |
| 110 | $3,270,000 | $2,081,081 |
| 111 | $3,300,000 | $2,098,098 |
| 112 | $3,330,000 | $2,115,115 |
| 113 | $3,360,000 | $2, |
Q: What is the purpose of the table used to calculate the present value of each payment?
A: The table is used to provide a clear and concise representation of the present value of each payment, allowing us to easily compare our calculations with the total calculated from the table.
Q: How does the table calculate the present value of each payment?
A: The table uses the formula for present value, which is PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.
Q: What is the interest rate used in the table?
A: The interest rate used in the table is 10%, which is a common interest rate used in financial calculations.
Q: How does the table calculate the total present value of all payments?
A: The table calculates the total present value of all payments by summing up the present value of each individual payment.
Q: What is the total present value of all payments calculated from the table?
A: The total present value of all payments calculated from the table is $878,611.
Q: How does the answer from part B compare to the total calculated from the table?
A: The answer from part B is $878,611, which is the same as the total calculated from the table.
Q: What does this comparison tell us about the accuracy of our calculations?
A: This comparison tells us that our calculations are accurate and reliable, as the answer from part B matches the total calculated from the table.
Q: What are some potential sources of error in present value calculations?
A: Some potential sources of error in present value calculations include:
- Incorrect interest rate
- Incorrect number of periods
- Incorrect future value
- Incorrect present value formula
Q: How can we minimize errors in present value calculations?
A: We can minimize errors in present value calculations by:
- Double-checking the interest rate and number of periods
- Verifying the future value and present value formula
- Using a reliable and accurate table or calculator
- Reviewing and revising our calculations as needed
Q: What are some real-world applications of present value calculations?
A: Present value calculations have many real-world applications, including:
- Evaluating investment opportunities
- Determining the value of a business or asset
- Calculating the cost of capital
- Making informed financial decisions
Q: How can we use present value calculations to make informed financial decisions?
A: We can use present value calculations to make informed financial decisions by:
- Evaluating the present value of different investment opportunities
- Determining the value of a business or asset
- Calculating the cost of capital
- Comparing the present value of different financial options
Q: What are some common mistakes to avoid when using present value calculations?
A: Some common mistakes to avoid when using present value calculations include:
- Incorrect interest rate
- Incorrect number of periods
- Incorrect future value
- Incorrect present value formula
- Not considering inflation or other factors that may affect the present value calculation.