Use the table Future Value of an Ordinary Annuity for $1.00 per Period on p. 39 to complete the table.
| Deposit | Rate | Compounded | Years | Number of Periods | Rate per Period | Table Value | FV of Ordinary Annuity | Interest Earned | A |
| --------- | ------- | ------------ | ----- | ----------------- | --------------- | ----------- | ---------------------- | --------------- | --- |
| $5,000 | 6.00% | Quarterly | 2 | a. 8 | b. 0.015 | c. 8.4326 | d. 42,163 | e. 2163 | A. |
| $800 | 4.0096 | Semiannually | 6 | a. 12 | b. 0.02 | c. 13.412 | d. 10,729.60 | e.1,129.60 | f. |
| $2,000 | 4.00% | Annually | 10 | a. 10 | b. 0.04 | c.12.006 | d. 24,012 | e. 4,012 | f. |
| $1,000 | 6.00% | Monthly | 3 | a. 36 | b. 0.005 | c. 39.336 | d. 39,336 | e. 3,336 | f. |
Answer (2)
Verify the consistency of each row using the formula: Future Value of Ordinary Annuity = Deposit * Table Value.
Calculate the Interest Earned using: Interest Earned = Future Value of Ordinary Annuity - (Deposit * Number of Periods).
Confirm that all provided values align with the calculated values for each row.
Conclude that the table is already complete and accurate, requiring no corrections: Table is complete and accurate .
Explanation
Understanding the Problem We are given a table related to the future value of an ordinary annuity and need to complete it using the provided information and the Future Value of an Ordinary Annuity table. The key formula to remember is:
Future Value of Ordinary Annuity = Deposit * Table Value
Also, the interest earned can be calculated as:
Interest Earned = Future Value of Ordinary Annuity - (Deposit * Number of Periods)
Analyzing Row 1 Let's analyze each row of the table and fill in the missing values.
Row 1: Deposit = $5,000 Rate = 6.00% compounded quarterly Years = 2 Number of Periods = 2 years * 4 quarters/year = 8 Rate per Period = 6.00% / 4 = 1.5% = 0.015 Table Value = 8.4326 Future Value of Ordinary Annuity = $5,000 * 8.4326 = $42,163 Interest Earned = $42,163 - ($5,000 * 8) = $42,163 - $40,000 = $2,163
All values in Row 1 are consistent.
Analyzing Row 2 Row 2: Deposit = $800 Rate = 4.00% compounded semiannually Years = 6 Number of Periods = 6 years * 2 semiannual periods/year = 12 Rate per Period = 4.00% / 2 = 2% = 0.02 Table Value = 13.412 Future Value of Ordinary Annuity = $800 * 13.412 = $10,729.60 Interest Earned = $10,729.60 - ($800 * 12) = $10,729.60 - $9,600 = $1,129.60
All values in Row 2 are consistent.
Analyzing Row 3 Row 3: Deposit = $2,000 Rate = 4.00% compounded annually Years = 10 Number of Periods = 10 years * 1 annual period/year = 10 Rate per Period = 4.00% / 1 = 4% = 0.04 Table Value = 12.006 Future Value of Ordinary Annuity = $2,000 * 12.006 = $24,012 Interest Earned = $24,012 - ($2,000 * 10) = $24,012 - $20,000 = $4,012
All values in Row 3 are consistent.
Analyzing Row 4 Row 4: Deposit = $1,000 Rate = 6.00% compounded monthly Years = 3 Number of Periods = 3 years * 12 months/year = 36 Rate per Period = 6.00% / 12 = 0.5% = 0.005 Table Value = 39.336 Future Value of Ordinary Annuity = $1,000 * 39.336 = $39,336 Interest Earned = $39,336 - ($1,000 * 36) = $39,336 - $36,000 = $3,336
All values in Row 4 are consistent.
Conclusion Since all the calculations and values provided in the table are consistent with the formulas and given data, there are no corrections needed. The table is already complete and accurate.
Examples
Understanding the future value of an annuity is crucial in financial planning. For instance, if you plan to deposit a fixed amount regularly into a retirement account, this calculation helps you estimate the total value of your investment at retirement. By knowing the interest rate, compounding frequency, and the number of periods, you can project the future value and make informed decisions about your savings strategy. This concept is also applicable in calculating loan payments, where understanding the annuity helps in determining the periodic payments required to pay off the loan within a specific timeframe.
The table for the future value of an ordinary annuity has been analyzed row by row, and each value has been verified using specific formulas. All calculated values for future values and interest earned are consistent with the formulas provided. Therefore, the conclusion is that the table is complete and accurate.
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