Complete the following using present value. (Use the Table 12.3 provided.) Note: Do not round intermediate calculations. Round the "Rate used" to the nearest tenth percent. Round the "PV factor" to 4 decimal places and final answer to the nearest dollar amount.
| Amount desired at end of period | Length of time | Rate | Compounded | On PV Table 12.3 | PV factor used | PV of amount desired at end of period |
|---|---|---|---|---|---|---|
| | 8 years | 3 | Semiannually | Period used | Rate used | |
Answer (1)
Calculate the number of periods: 8 years × 2 = 16 periods .
Calculate the rate per period: 2 3% = 1.5% .
Find the PV factor: From the PV table (or calculation), the PV factor for 16 periods at 1.5% is 0.7880.
Calculate the present value: P V = A × 0.7880 , where A is the amount desired at the end of the period. The final answer is 0.7880 A .
Explanation
Understanding the Problem We are asked to complete a present value table. The table requires us to determine the period used, rate used, PV factor used, and the present value of the amount desired at the end of the period.
Calculating the Number of Periods The length of time is 8 years, and the interest is compounded semiannually. This means the number of periods is 8 × 2 = 16 .
Calculating the Rate per Period The annual interest rate is 3%, compounded semiannually. Therefore, the rate per period is 2 3% = 1.5% .
Finding the PV Factor Looking at the PV table 12.3 (not provided, but we can calculate it), for 16 periods at a rate of 1.5%, the PV factor is approximately 0.7880. This can be calculated as ( 1 + 0.015 ) 16 1 ≈ 0.7880 .
Calculating the Present Value To find the present value (PV) of the amount desired at the end of the period, we multiply the amount desired by the PV factor. Let's assume the amount desired at the end of the period is A . Then, the present value is P V = A × 0.7880 . Since the amount desired at the end of the period is not specified in the table, we cannot calculate a numerical value for the PV. However, we can express it in terms of A.
Completing the Table Filling in the table:
Amount desired at end of period
Length of time
Rate
Compounded
On PV Table 12.3
PV factor used
PV of amount desired at end of period
$A
8 years
3%
Semiannually
Period used: 16, Rate used: 1.5%
0.7880
$0.7880A
Final Answer Without knowing the amount desired at the end of the period, we can only express the present value in terms of A . The period used is 16, the rate used is 1.5%, and the PV factor is 0.7880. Therefore, the present value of the amount desired at the end of the period is 0.7880 A .
Examples
Present value calculations are essential in financial planning. For example, if you want to have $10,000 in a savings account after 5 years with a certain interest rate, you can use present value calculations to determine how much money you need to deposit today. This helps in setting realistic savings goals and making informed investment decisions. Understanding present value is also crucial in evaluating the profitability of long-term projects and investments.
