payments are known as lump sums. We can solve for the future value or the present value of a lump sum as we discuss below.

Finding the future value $($FV$),$ or

$,$ is the process of going from today's values to future amounts. The FV equation is:

$F{V}_N=PV(1+I{)}^N$

Here, $PV=$ present value; I $=$ interest rate per year, and $N=$ number of periods. You can use calculators and spreadsheets to find future values. A graph of the

process shows how any sum grows over time at various interest rates. The greater the interest

rate, the $,$ the growth rate.

Finding the present value $($PV$)$ is called discounting, and it is simply the reverse of

equation is:

In general, the present value of a cash flow due $N$ years in the future is the amount which, if it were on hand today, would grow to equal the given future amount. The $PV$

Present value $=PV=\frac{F{V}_N}{(1+1{)}^N}$

A graph of the discounting process shows how the present value of any sum to be received in the future decreases and approache: as the years to receipt increases, and the present value declines faster at

financial management is to maximize the firm's value, and the value of any asset is the

$|$ value of its expected future cash flows.

One can solve for either the interest rate or the number of periods using the FV and the PV equations. The easiest way to solve for these variables is with a financial calculator or a spreadsheet,

intermediate calculations. Round your answer to the nearest cent.

$

Do not round intermediate calculations. Round your answer to the nearest cent.

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