Complete the following using present value. (Use 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 | Length of time | Rate | Compounded | On PV Table 12.3 | PV factor used | PV of amount desired at end of period |
|---|---|---|---|---|---|---|
| $19,100 | 7 years | 20% | Quarterly | Period used: 28, Rate used: 5% | 0.2551 | ? |
Answer (2)
The present value of $19,100 desired at the end of 7 years, using a PV factor of 0.2551, is calculated to be $4,872.41. This is done by multiplying the amount by the PV factor. Thus, $4,872.41 represents the value today needed to achieve $19,100 in the future, given the specified rate and time.
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Multiply the amount desired at the end of the period by the present value factor.
The amount desired is $19,100 and the PV factor is 0.2551.
Calculate the present value: $PV = $19,100 \times 0.2551 = $4872.41.
The present value of the amount desired at the end of the period is $4872.41 .
Explanation
Understanding the Problem We are asked to calculate the present value (PV) of an amount desired at the end of a period. We are given the amount desired at the end of the period, the length of time, the interest rate, how it is compounded, and the present value factor. We need to multiply the amount desired by the present value factor to find the present value.
Setting up the Calculation The formula for present value (PV) is: P V = Amount desired × PV factor We are given:
Amount desired at the end of the period = $19,100
PV factor = 0.2551
Calculating the Present Value Now, we plug in the given values into the formula: PV = $19,100 \times 0.2551 PV = $4872.41
Final Answer Therefore, the present value of the amount desired at the end of the period is $4872.41.
Examples
Understanding present value is crucial in many financial decisions. For instance, when considering an investment that promises a future payout, calculating the present value helps determine how much that future payout is worth today. This allows investors to compare different investment opportunities and make informed decisions. For example, if you are promised $10,000 in 5 years with an interest rate of 5% compounded annually, you can calculate the present value to see how much you should invest today to reach that goal. This concept is also useful in evaluating loans, mortgages, and other financial products.
