An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
The period used is 20 and the rate used is 8%.
The PV factor from the table is 0.2145.
The present value (PV) is calculated as P V = A × 0.2145 .
The present value of the amount desired at the end of the period is 0.2145 A .
Explanation
Understanding the Problem We are given a present value problem where we need to find the present value of an amount desired at the end of 20 years, with an interest rate of 8% compounded annually. We will use the present value (PV) factor from Table 12.3 to calculate the present value. Since the amount desired at the end of the period is not given, we will assume it to be A .
Finding the PV Factor The length of time is 20 years, so the period used is 20. The rate is 8%, so the rate used is 8%. We look up the PV factor in Table 12.3 for a period of 20 and a rate of 8%. The PV factor is 0.2145.
Calculating the Present Value The PV factor is 0.2145. We calculate the present value (PV) of the amount desired at the end of the period using the formula P V = A × f , where A is the amount desired at the end of the period and f is the PV factor. Therefore, P V = A × 0.2145 = 0.2145 A .
Final Answer Since the amount desired at the end of the period is not specified, we cannot determine a numerical value for the present value. However, we can express the present value in terms of A . The PV factor used is 0.2145, and the present value of the amount desired at the end of the period is 0.2145 A .
Examples
Present value calculations are essential in financial planning. For example, if you want to have $10,000 in 20 years with an 8% annual return, you can use present value to determine how much you need to invest today. This concept is also used in evaluating investment opportunities, loan calculations, and retirement planning, helping individuals and businesses make informed financial decisions by understanding the time value of money.
