# How is the Future Value Calculated?

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According to the time value of money, a dollar in hand today is worth more than a dollar received at a certain point in the future. That’s because you can take today’s dollar and invest it to earn interest and capital gains. The future value is a way of calculating the amount that an investment made today would grow to when invested at a specific interest rate. It represents how much an investor would need to receive at a future time in order to compensate for the lost opportunity cost of not being able to invest his money today.

#### TL;DR (Too Long; Didn't Read)

Future value determines how much the present value of cash will be worth at a specified point in the future. It’s calculated using a simple mathematical formula.

## Future Value Explained

Future value is a simple formula used to figure out how much an amount of cash will be worth at a specific point in the future. The idea is that \$100 today is not worth \$100 in a year’s time due to the time value of money – you could invest the \$100 at a 3 percent interest rate, for example, and have \$103 next year. The future value formula also calculates the effect of compound interest. Earning 0.25 percent per month is not the same as earning 3 percent per year because you can reinvest each month’s earnings to create additional income.

## Future Value Example

Suppose you are investing \$10,000 today in an account that earns 10 percent interest, compounded annually. In year one, your investment would grow by \$1,000 – that’s 10 percent of \$10,000 – to \$11,000. At the end of two years, the \$10,000 investment will have grown to \$12,100. Note how the investment earned \$1,100 in the second year but only \$1,000 during the first year. That’s because the interest is compounded, so you’re earning interest on the previous year’s cumulative account balance. In this example, the future value of your \$10,000 investment is \$12,100 after two years.

## Calculating Future Value

The equation for finding the future value of an investment earning compounding interest is:

FV = I (1 + R)t

Where:

• FV  is the future value at the end of year t.
• I is the initial investment.
• R is the annually compounded interest rate.
• t is the number of years.

Using this formula, you can calculate the future value of your \$10,000 investment in year 5 as follows:

FV = 10,000 (1 + 0.10)5 = \$16,105.10.

## Future Value Formula in Excel

Sometimes, an investor will need to calculate the future value of money when she’s making a series of deposits over a number of periods, rather than a one-time investment. Excel’s FV function is useful here because it includes additional parameters accounting for the time value of periodic payments. Suppose, for example, an investor deposits \$2,000 per year over five years at a 10 percent interest rate, instead of investing \$10,000 in one go. Excel’s FV formula looks like this:

FV(rate, nper, pmt, [pv], [type])

Where:

• Rate – the interest rate, 10 percent in our example.
• Nper – the number of periods over which an investment is made, 5 in our example.
• Pmt – the principal payment made each period, or \$2,000.
• Pv – the present value of cash that you have today. In this example, it’s zero, since our investor has not made an investment yet.
• Type – this indicates whether payments are made at the beginning or end of a period; set this to 0 for payments made at the end of a period and 1 for payments made at the beginning.

In this example, plugging the numbers into Excel gives a future value of FV (0.1, 5, 2,000, 0, 1) = \$13, 431.22.