**Formula For The Future Value Of An Annuity** – Most of us have experience with a series of fixed payments over a period of time – such as rent or car payments – or receiving several payments over a period of time, such as interest on bonds or certificates of deposit. (CD). These continuous or recurring payments are technically called “annuities” (not to be confused with financial products called annuities, although the two are related).

There are several ways to measure the cost of these payments or their value. Here’s what you need to know about calculating the present value (PV) or future value (FV) of an annuity.

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## Formula For The Future Value Of An Annuity

Annuities, in the sense of this word, are divided into two basic types: ordinary annuities and due annuities.

### Time Value Of Money — Tables Of Factors

You can calculate the present or future value of an ordinary annuity or an annuity due using the following formula.

Future value (FV) is a measure of how much a series of regular payments will be worth at some point in the future, given a particular interest rate. So, for example, if you plan to invest a certain amount every month or year, this will tell you how much you will accumulate in the future. If you make regular loan payments, the future value will be useful in determining the total cost of the loan.

Because of the time value of money—the concept that any amount is worth more now than it will be in the future because it can then be invested—the first $1,000 payment is worth more than the second, and so on. So, let’s say you invest $1,000 a year for the next five years, at 5% interest. Below is how much you will have at the end of the five year period.

Instead of calculating each payment one by one and then adding them all up, you can use the following formula to tell you how much money you’ll end up with:

### Calculating Present And Future Value Of Annuities

Note that the one-cent difference in this result, $5,525.64 versus $5,525.63, is due to rounding in the first calculation.

Unlike the future value calculation, the present value (PV) calculation tells how much money will be needed now to produce a series of payments in the future, again assuming a fixed interest rate.

Using the same example of five payments of $1,000 made over five years, this would look like a present value calculation. It shows that $4,329.58, invested at 5% interest, will be enough for these five $1,000 payments.

A paying annuity, you will recall, differs from an ordinary annuity in that the annuity payments are made at the beginning, rather than the end, of each period.

## Annuity Contracts For Investment Or For Creating Income Stream

To account for the payments that occur at the beginning of each period, a slight modification to the formula used to calculate the future value of an ordinary annuity is required and results in a higher value, as shown below.

The reason for the higher value is that payments made early in the period have more time to earn interest. For example, if $1,000 is invested on January 1st instead of January 31st, it will have another month to grow.

Note again that the one cent difference in this result, $5,801.92 vs. $5,801.91, is due to rounding in the first calculation.

In addition, the formula for calculating the present value of an annuity because it takes into account the fact that the payment is made at the beginning and not at the end of each period.

#### Compound Interest And Present Value

For example, you can use this formula to calculate the present value of future rent payments, as specified in your lease. Let’s say you pay $1,000 a month. Below we can see how much it will cost in five months, in present value, if you keep your money in an account that earns 5% interest.

The formula described above makes it possible — and relatively easy, if you don’t remember the math — to determine the present or future value of an ordinary annuity or an annuity due. Excel can help calculate the PV of fixed annuities. Financial calculators (you can find them online) also have the ability to calculate for you with accurate data.

The offers that appear in this table come from partnerships for which you are compensated. This fee may affect how and where ads appear. excluding all offers available on the market. Although your retirement is probably still a long way off, the sooner you start investing, the more you can harness the power of compound interest to build your savings.

Were you surprised to learn in Section 10.5 that your annual gross retirement income should be $160,000 by age 65? How long will you live? The average life expectancy of Canadians is about 80 years; If you reach that age, you will need 15 years of pension. Using a conservative interest rate of 5% per year along with 3% annual inflation, that translates to roughly $2 million in savings by the time you retire. A difficult goal, isn’t it? You might ask yourself, “If I started saving $300 a month today, would it be enough?”

### Appendix: Present Value Tables

Obviously, knowing how much your annuity will be worth in the future is important. This is not only important for investments, but also for loans, since most companies and individuals repay loans through an annuity structure. After several annuity payments, how will you know if you or your company still has outstanding debt?

In the previous section, you learned to identify the basic characteristics of an annuity, so you can now begin to solve any annuity for any unknown variable. There are four annuity formulas. This section covers the first two, which calculate future values for ordinary annuities and annuities due. The formula includes simple and ordinary annuities.

The future value of any annuity is equal to the sum of all the future values of all the annuity payments when moved to the end of the last payment interval. For example, suppose you invest $1,000 at the end of each year for the next three years in an investment that returns 10% annually. This is a common simple annuity because the payment takes place at the end of the interval, and the frequency of calculation and payment is the same. If you want to know how much money you have in your investment after three years, the figure below illustrates how you would use the basic concept of the time value of money to move each payment amount to a future date (the focus date) and add the value to get the future value.

Although you can use this technique to handle all annuity situations, the calculations become more complicated as the number of payments increases. In the above example, what if the person makes a monthly contribution of $250? There are 12 payments over three years, resulting in 11 separate future value calculations. Or if they pay monthly, 36 payments over three years will result in 35 separate future value calculations! It is clear that it will be difficult and time-consuming – no one is prone to mistakes. There has to be a better way!

#### Annuity Formula Present Value Ppt Powerpoint Presentation Infographics Cpb

The formula for the future value of an ordinary annuity is actually easier and faster than performing a series of future value calculations for each payment. However, at first glance, the formula is quite complex, so the various parts of the formula are studied in detail before they are assembled.

The annuity formula is a more complicated version of the rate, installment, and basis formula presented in Chapter 2. The formula related to 2.2 and the first payment in the figure above gives the following:

This equivalent level becomes a very complex expression that is studied in three parts: the total percentage variation, the percentage variation with each payment, and the quotient.

Step 4: If (PV ) = 0 $, go to step 5. If there is a non-zero value for (PV ), it is considered a one-time payment. Use formula 9.2 to determine (N) since this is not an annuity calculation. Move the current value to the end of the time slice using formula 9.3.

#### Solution: Mathematics Of Investment Deferred Annuity

Calculate the future value. If you calculated the future value in step 4, combine the future values from steps 4 and 5 to get the total future value.

Going back to the RRSP scenario from the beginning of this section, let’s say you’re 20 years old and invest $300 at the end of each month for the next 45 years. You haven’t started an RRSP and don’t have an opening balance. A fixed interest rate of 9% compounded monthly on the RRSP is possible.

Step 1: This is a simple ordinary annuity because the frequency coincides and the payments occur at the end of the payment interval.

Step 2: The known variables are (PV) = $0, (IY) = 9%, (CY) = 12, (PMT) = $300, (PY) =

#### Chapter The Time Value Of Money Mcgraw Hill/irwin

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