Future Value of an Ordinary Annuity: Definition and How to Calculate It

In the previous article, we have covered the future value of an annuity due. In this article, we cover the future value (FV) of an ordinary annuity. This includes the key definition, how to calculate it as well as how to generate the future value of an ordinary annuity table.

So let’s dive in!

What is Future Value of an Ordinary Annuity?

The future value of an ordinary annuity refers to the future returns of periodic equal cash flows that occur at the end of each period. This future return comes from the sum of compound interest of each cash flow of invested funds at the end of the lifetime of such annuity.

How to Calculate Future Value of an Ordinary Annuity?

In order to calculate the future value of an ordinary annuity, we can simply use the FV interest factors of an ordinary annuity multiply with the annuity of cash flow. Below is the FV of an ordinary annuity formula:

FVA= PMT × FVIFA _{i, n}

Where:

PMT = Periodic cash flow of annuity

FVIFA = FV interest factors of an ordinary annuity

i = Annual nterest

n = Number of years

In the above formula, we need to have the future value of an ordinary table to find the FV interest factors of ordinary annuity.

We can break it down into detail formula as below:

FVA = PMT × [((1+i)ⁿ -1) /i]

Where:

[((1+i)ⁿ -1) /i] is the detail of FV interest factors of an ordinary annuity.

We can also calculate the future value of an ordinary annuity by using the Excel spreadsheets. In the below section, we will give an example of how to calculate the FV of an ordinary annuity by using both the above formula and Excel Spreadsheets.

Example

Suppose Peter is considering investing in an ordinary annuity of 5 years for $1,000 each. This annuity has an annual compound interest of 8% and he wants to know how much he would get at the end of year 5.

Calculate the FV of ordinary annuity above.

We can calculate the FV of ordinary annuity above in three different ways as mentioned above.

The first calculation is by looking at the future value of an ordinary annuity table and then substitute the FV interest factors of an ordinary annuity into the formula.

FVA= PMT × FVIFA _{i, n}

Where:

PMT = $1,000

FVIFA _{8%, 5 Yrs} = 5.867 (As per the future value of an ordinary annuity table)

Thus, FVA = 1,000 × 5.867 = $5,867

In the second formula, we need to use the financial calculator.

FVA = PMT × [((1+i)ⁿ -1) /i]

Where:

PMT = $1,000

i = 8%

n = 5 years

Therefore, FVA = 1,000 × [((1+0.08)⁵ -1) /0.08] = $5,867

In the third method, we can calculate the FV of an ordinary annuity by using Excel spreadsheet as follows:

The table above provides an illustration of how to can calculate the FV of an ordinary annuity by using Excel spreadsheets. So you can look at the Excel formula at the bottom of the table.

As you can see, the three methods above provide the same amount of the future returns of the ordinary annuity. Thus, you can use any methods of convenience for you.

How to Generate Future Value of an Ordinary Annuity Table?

We can generate the future value of an ordinary annuity table by using the formula below:

FVIFA = ((1+i)ⁿ -1)/i

By using the formula above, we can generate the future value of an ordinary due table as below:

Period	1%	2%	3%	4%	5%	6%	7%	8%	9%	10%
1	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
2	2.010	2.020	2.030	2.040	2.050	2.060	2.070	2.080	2.090	2.100
3	3.030	3.060	3.091	3.122	3.153	3.184	3.215	3.246	3.278	3.310
4	4.060	4.122	4.184	4.246	4.310	4.375	4.440	4.506	4.573	4.641
5	5.101	5.204	5.309	5.416	5.526	5.637	5.751	5.867	5.985	6.105
6	6.152	6.308	6.468	6.633	6.802	6.975	7.153	7.336	7.523	7.716
7	7.214	7.434	7.662	7.898	8.142	8.394	8.654	8.923	9.200	9.487
8	8.286	8.583	8.892	9.214	9.549	9.897	10.260	10.637	11.028	11.436
9	9.369	9.755	10.159	10.583	11.027	11.491	11.978	12.488	13.021	13.579
10	10.462	10.950	11.464	12.006	12.578	13.181	13.816	14.487	15.193	15.937
11	11.567	12.169	12.808	13.486	14.207	14.972	15.784	16.645	17.560	18.531
12	12.683	13.412	14.192	15.026	15.917	16.870	17.888	18.977	20.141	21.384
13	13.809	14.680	15.618	16.627	17.713	18.882	20.141	21.495	22.953	24.523
14	14.947	15.974	17.086	18.292	19.599	21.015	22.550	24.215	26.019	27.975
15	16.097	17.293	18.599	20.024	21.579	23.276	25.129	27.152	29.361	31.772

Conclusion

To sum up, the future value of an ordinary annuity is the future returns of periodic equal cash flows occur at the end of each period. We can calculate the future returns of such annuity by using the future value of an ordinary table, the detail formula as well as in Excel spreadsheets. All these methods provide the future returns of the ordinary annuity.