Complete the following using present value. (Use the Table 12.3.) Note: Do not round intermediate calculations. Round the "PV factor" to 4 decimal places and final answer to the nearest cent. Amount desired at end of period $ 18.500 Length of time 5 years Rate Compounded 8 % Quarterly On PV Table 12.3 Period used Rate used PV factor used PV of amount desired at end of period

FINANCIAL ACCOUNTING
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Chapter1: Financial Statements And Business Decisions
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This image shows a table titled "Present value interest factor of $1 per period at i% for n periods, PVIF(i,n)." The table is organized to present the present value interest factors for various interest rates (i%) over multiple periods (n). 

### Table Structure:
1. **Row Headers (Periods):** 
   - The first column lists the periods, ranging from 1 to 40.

2. **Column Headers (Interest Rates):** 
   - The first row lists different interest rates ranging from 0.5% to 10.0% in increments of 0.5%.

3. **Table Body:**
   - The body of the table contains numerical values representing the present value interest factor (PVIF) for each combination of interest rate and period. These factors are used in finance to determine the present value of a series of future cash flows.

### Example:
- For a period of 1 year and an interest rate of 0.5%, the PVIF is 0.9950.
- For a period of 10 years and an interest rate of 5.0%, the PVIF is 0.6139.

### Understanding the Table:
- The PVIF decreases as either the period increases or the interest rate rises, reflecting the time value of money principle: the present value of future cash flows decreases the further into the future they are or the higher the discount rate.

This table is a valuable tool for calculating the present value of annuities or other financial instruments with similar cash flow structures.
Transcribed Image Text:This image shows a table titled "Present value interest factor of $1 per period at i% for n periods, PVIF(i,n)." The table is organized to present the present value interest factors for various interest rates (i%) over multiple periods (n). ### Table Structure: 1. **Row Headers (Periods):** - The first column lists the periods, ranging from 1 to 40. 2. **Column Headers (Interest Rates):** - The first row lists different interest rates ranging from 0.5% to 10.0% in increments of 0.5%. 3. **Table Body:** - The body of the table contains numerical values representing the present value interest factor (PVIF) for each combination of interest rate and period. These factors are used in finance to determine the present value of a series of future cash flows. ### Example: - For a period of 1 year and an interest rate of 0.5%, the PVIF is 0.9950. - For a period of 10 years and an interest rate of 5.0%, the PVIF is 0.6139. ### Understanding the Table: - The PVIF decreases as either the period increases or the interest rate rises, reflecting the time value of money principle: the present value of future cash flows decreases the further into the future they are or the higher the discount rate. This table is a valuable tool for calculating the present value of annuities or other financial instruments with similar cash flow structures.
To complete the table, calculate the present value using the provided parameters and Table 12.3. 

1. **Amount desired at end of period:** $18,500
2. **Length of time:** 5 years
3. **Rate:** 8%
4. **Compounded:** Quarterly

**Steps:**

- **Period used:** Since interest is compounded quarterly over 5 years, calculate the number of periods: \(5 \times 4 = 20\) periods.
- **Rate used:** Divide the annual rate by the number of compounding periods in a year: \(\frac{8\%}{4} = 2\%\) per period.

**On PV Table 12.3:**

- **PV factor used:** Look up the PV factor for 20 periods at a 2% rate from Table 12.3. (This value would be provided in the table and used for precise calculations.)

**Final calculation:**

- Use the formula: 
  \[
  PV = \text{Amount desired} \times \text{PV factor}
  \]
- **PV of amount desired at end of period:** Calculate and round to the nearest cent.

**Note:** Ensure all intermediate calculations are not rounded until the final step, where the PV factor is rounded to four decimal places.

This exercise demonstrates the application of the present value concept to determine how much needs to be invested today to achieve a future financial goal, considering compounding intervals.
Transcribed Image Text:To complete the table, calculate the present value using the provided parameters and Table 12.3. 1. **Amount desired at end of period:** $18,500 2. **Length of time:** 5 years 3. **Rate:** 8% 4. **Compounded:** Quarterly **Steps:** - **Period used:** Since interest is compounded quarterly over 5 years, calculate the number of periods: \(5 \times 4 = 20\) periods. - **Rate used:** Divide the annual rate by the number of compounding periods in a year: \(\frac{8\%}{4} = 2\%\) per period. **On PV Table 12.3:** - **PV factor used:** Look up the PV factor for 20 periods at a 2% rate from Table 12.3. (This value would be provided in the table and used for precise calculations.) **Final calculation:** - Use the formula: \[ PV = \text{Amount desired} \times \text{PV factor} \] - **PV of amount desired at end of period:** Calculate and round to the nearest cent. **Note:** Ensure all intermediate calculations are not rounded until the final step, where the PV factor is rounded to four decimal places. This exercise demonstrates the application of the present value concept to determine how much needs to be invested today to achieve a future financial goal, considering compounding intervals.
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