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The future value of an annuity is the amount calculated by applying a specific rate of return or discount rate to a set of periodic payments at a specific date in the future. The higher the discount rate, the greater the annuity's future value.
The future value of an annuity is the amount calculated by applying a specific rate of return or discount rate to a set of periodic payments at a specific date in the future. The higher the discount rate, the greater the annuity's future value. The future value of an annuity can be calculated as long as the annuity-related variables, such as payment amount, expected rate of return, and payment period, are known.
Due to the time value of money, funds received or paid today are worth more than the same amount of money in the future. This is because money can be invested and grow over time. By the same logic, a one-time payment of 1,000 annuity payments spread out over five years.
The formula for the future value of an ordinary annuity is as follows. (An ordinary annuity pays interest at the end of a specified period, while an annuity payable pays interest at the beginning of the period.)
<!-- @@@ -->Important Note: Ordinary annuities are more common, but all else being equal, the future value of an annuity payable tends to be higher.
In an annuity payable, payments are made at the beginning of each period. Therefore, the formula is slightly different. To calculate the future value of the annuity payable, simply multiply the above formula by (1 + r):
<!-- @@@ -->Suppose someone decides to invest $125,000 each year for the next five years in an annuity with an expected annual compound return of 8%.
In this example, the series of payments is an ordinary annuity, with payments made at the end of each period. Using the above formula, the expected future value is as follows:
<!-- @@@ -->733,325 \ \end{aligned} $$
We use the same example above, but with an annuity payable. This means that each payment of $125,000 is made at the beginning of each period. Its future value is calculated as follows:
<!-- @@@ -->791,991 \ \end{aligned} $$
All else being equal, an annuity payable has a higher future value than a regular annuity because the funds have extra time to accumulate compound interest. In this example, the future value of the annuity payable is $58,666 more than an ordinary annuity.
When calculating future value, one component is called the future value factor. The future value factor refers to a lump sum or the total increase in a series of cash flows. For example, if the future value of 1,100, the future value factor is 1.1. A future value factor of 1.0 means that the current value of this set of cash flows is equal to its value today.
Annuity payments are usually made at the end of each period, while annuity payments are payable at the beginning of each period. While this may not seem like a significant difference, there may be a considerable difference between the two when considering the accumulation of interest.
Present value and future value represent the value of an investment looking forward or looking back. There is a direct relationship between these two concepts because the future value of a series of cash flows also has a present value. For example, the present value of 1,200 today.
Often, investors and analysts will know one value and try to solve for another. For example, if you buy a stock that earns 2% annually for 10,000 in hand when you make a down payment on a car next year, you can solve for its present value.
An annuity is a series of payments made over a period of time, usually the same amount each period. Investors can determine the future value of their annuity by considering the annuity amount, expected rate of return, and payment period. Additionally, whether annuity payments are made at the beginning or end of the period also affects the calculation of its future value.
[1] California State Board of Equalization. "Time Value of Money – Six Functions of a Dollar - Lesson 10 – Annuities."
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重要提示： 普通年金更为常见，但在其他条件相同的情况下，应付年金的未来价值往往更高。
在应付年金中，支付是在每个期初进行的。因此，公式略有不同。要计算应付年金的未来价值，只需将上述公式乘以（1 + r）：
年金的未来价值是指在未来某一特定日期，将一组定期支付的金额按照特定的收益率或折现率计算后得到的金额。折现率越高，年金的未来价值越大。只要年金相关的变量（如支付金额、预期收益率和支付期限）都已知，就可以计算出年金的未来价值。
由于货币的时间价值，今天收到或支付的资金比未来同样数量的资金更具价值。这是因为资金可以进行投资并随时间增长。根据同样的逻辑，今天的一次性支出5000美元的价值将高于分五年支付的五笔1000美元的年金付款总和。
普通年金的未来价值公式如下。（普通年金在特定期间结束时支付利息，而应付年金则在期初支付。）
\begin{aligned} \text{未来价值} &= \$125,000 \times \frac { \big ( ( 1 + 0.08 ) ^ 5 - 1 \big ) }{ 0.08 } \\ &= \$733,325 \\ \end{aligned} $$$125,000 \times \frac { \big ( ( 1 + 0.08 ) ^ 5 - 1 \big ) }{ 0.08 } \\ &= \$733,325 \\ \end{aligned}
我们使用上述相同的例子，但使用的是应付年金。这意味着每笔125,000美元的支付都是在每个期初进行的。其未来价值则计算如下：
$$ \begin{aligned} \text{未来价值} &= $125,000 \times \frac { \big ( ( 1 + 0.08 ) ^ 5 - 1 \big ) }{ 0.08 } \times ( 1 + 0.08 ) \ &= $791,991 \ \end{aligned} $$$125,000 \times \frac { \big ( ( 1 + 0.08 ) ^ 5 - 1 \big ) }{ 0.08 } \times ( 1 + 0.08 ) \ &= $
重要提示： 普通年金更为常见，但在其他条件相同的情况下，应付年金的未来价值往往更高。
在应付年金中，支付是在每个期初进行的。因此，公式略有不同。要计算应付年金的未来价值，只需将上述公式乘以（1 + r）：
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