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First, consider future value. Future value (FV) refers to the amount of money to which an investment will grow over a finite period of time at a given interest rate. Put another way, future value is the cash value of an investment at a particular time in the future. Start by considering the simplest case, a single-period investment.

Investing For a Single Period:

Suppose you invest $100 in a savings account that pays 10 percent interest per year. How much will you have in one year? You will have $110. This $110 is equal to your original principal of $100 plus $10 in interest. We say that $110 is the future value of $100 invested for one year at 10 percent, meaning that $100 today is worth $110 in one year, given that the interest rate is 10 percent.

In general, if you invest for one period at an interest rate r, your investment will grow to (1 + r) per dollar invested. In our example, r is 10 percent, so your investment grows to 1 + .10 = 1.10 dollars per dollar invested. You invested $100 in this case, so you ended up with $100 x 1.10 = $110.

Investing For More Than One Period:

Consider your $100 investment that has now grown to $110. If you keep that money in the bank, what will you have after two years, assuming the interest rate remains the same? You will earn $110 x .10 = $11 in interest after the second year, making a total of $100 + $11 = $121. This $121 is the future value of $100 in two years at 10 percent. Another way of looking at it is that one year from now, you are effectively investing $110 at 10 percent for a year. This is a single-period problem, so you will end up with $1.10 for every dollar invested, or $110 x 1.1 = $121 total.

This $121 has four parts. * The first part is the first $100 original principal. * The second part is the $10 in interest you earned in the first year. * The third part, is the other $10 you…...

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