# Present Value And Future Value Of An Annuity, Net Present Value, With Formulas And Examples

Against the annuity payment A, or by using a graphing calculator, and graphing the value of the annuity payment as a function of interest for a given present value. In the latter case, the interest rate is where the line representing the rate of interest intersects the line for the annuity payment. The formula for finding the present value of an ordinary annuity is often presented one of two ways, where “r” represents the interest rate and “n” represents the number of periods. An annuity table, or present value table, is simply a tool to help you calculate the present value of your annuity. Figuring the present value of any future amount of an annuity may also be performed using a financial calculator or software built for such a purpose. ​An annuity due, you may recall, differs from an ordinary annuity in that the annuity due’s payments are made at the beginning, rather than the end, of each period.

• As any expert in financial literacy will attest, your balance sheet is the foundation for everything from your budget to your retirement savings.
• To account for payments occurring at the beginning of each period, it requires a slight modification to the formula used to calculate the future value of an ordinary annuity and results in higher values, as shown below.
• David has helped thousands of clients improve their accounting and financial systems, create budgets, and minimize their taxes.
• You can calculate the present or future value for an ordinary annuity or an annuity due using the following formulas.

If you don’t have access to an electronic financial calculator or software, an easy way to calculate present value amounts is to use present value tables . PV tables cannot provide the same level of accuracy as financial calculators or computer software because they use factors that are rounded off to fewer decimal places. In addition, they usually contain a limited number of choices for interest rates and time periods.

To account for payments occurring at the beginning of each period, it requires a slight modification to the formula used to calculate the future value of an ordinary annuity and results in higher values, as shown below. You might want to calculate the future value of an annuity, to see how much a series of investments will be worth as of a future date. This is done by using an interest rate to add interest income to the amount of the annuity. The interest rate can be based on the current amount being obtained through other investments, the corporate cost of capital, or some other measure. The present value of an annuity is the current value of future payments from that annuity, given a specified rate of return or discount rate. These recurring or ongoing payments are technically referred to as “annuities” .

## The Future Value Of An Annuity

In contrast to the future value calculation, a present value calculation tells you how much money would be required now to produce a series of payments in the future, again assuming a set interest rate. Calculate the future value interest factor of an annuity and create a table of FVIFA values. Create a printable compound interest table for the future value of an ordinary annuity or future value of an annuity due for payments of \$1. The first column refers to the number of recurring identical payments in an annuity. The other columns contain the factors for the interest rate specified in the column heading. The point where a particular interest rate intersects a particular number of payments is the annuity’s PVOA factor. When you multiply this factor by the annuity’s recurring payment amount, the result is the present value of the annuity.

You’ve owned the annuity for five years and now have two annual payments left. You can find the exact present value of your remaining payments by using Excel. First, you need to know whether you receive your payments at the end of the period — as is the case with an ordinary annuity — or at the beginning of the period.

## Annuity Table

The future value of an annuity is the total value of payments at a specific point in time. David Kindness is a Certified Public Accountant and an expert in the fields of financial accounting, corporate and individual tax planning and preparation, and investing and retirement planning. David has helped thousands of clients improve their accounting and financial systems, create budgets, and minimize their taxes. In this example, you can see that both the payment and the present value are entered as negative values. A savings account is a typical account at a bank or a credit union that allows an individual to deposit, secure, or withdraw money when the need arises. A savings account usually pays some interest on deposits, although the rate is quite low. For example, using Excel, you can find the present value of an annuity with values that fall outside the range of those included in an annuity table.

Despite this, present value tables remain popular in academic settings because they are easy to incorporate into a textbook. Because of their widespread use, we will use present value tables for solving our examples. Present value tables aren’t as precise as manual calculations or financial software programs because the tables contain a limited set of interest rates and payments. If you take a look at a variety of ordinary annuity tables, you’ll see the factors are all within a decimal place, depending on whether they are rounded. Additionally, you can use them only with fixed payment amounts and interest rates. If you don’t have access to an electronic financial calculator or software, an easy way to calculate present value amounts is to use present value tables.

You can calculate the present or future value for an ordinary annuity or an annuity due using the following formulas. The present value is how much money would be required now to produce those future payments. Note that in using the present value or future value formula, either the payment or the present value or future value could be blank, or they can both have values, depending on the investment. Advance your career in investment banking, private equity, FP&A, treasury, corporate development and other areas of corporate finance.

Thus, Harvest Designs buys a warehouse from Higgins Realty for \$1,000,000, and promises to pay for the warehouse with five payments of \$200,000, to be paid at intervals of one payment per year; this is an annuity. If the payments are due at the end of a period, the annuity is called an ordinary annuity. If the payments are due at the beginning of a period, the annuity is called an annuity due. The NPV can also be calculated for a number of investments to see which investment yields the greatest return.

## Calculating The Future Value Of An Ordinary Annuity

Simply select the correct interest rate and number of periods to find your factor in the intersecting cell. That factor is then multiplied by the dollar amount of the annuity payment to arrive at the present value of the ordinary annuity. According to the concept of the time value of money, receiving a lump sum payment in the present is worth more than receiving the same sum in the future. As such, having \$10,000 today is better than being given \$1,000 per year for the next 10 years because the sum could be invested and earn interest over that decade. At the end of the 10-year period, the \$10,000 lump sum would be worth more than the sum of the annual payments, even if invested at the same interest rate.

Hence, if you pay at the beginning of each year instead of at the end, you will have \$24,159.95 more for your retirement. If a variable has no value, then simply insert an extra comma or semicolon to indicate no value for that variable. A pension fund is a fund that accumulates capital to be paid out as a pension for employees when they retire at the end of their careers. Here, the annuity value is higher; hence, it would be reasonable to choose the annuity over the lump-sum amount. The company can help you find the right insurance agent for your unique financial objectives. These reviewers are industry leaders and professional writers who regularly contribute to reputable publications such as the Wall Street Journal and The New York Times. Annuity.org partners with outside experts to ensure we are providing accurate financial content.

The easiest and most accurate way to calculate the present value of any future amounts is to use an electronic financial calculator or computer software. The following future value of annuity table (\$1 per period at r% for n periods) will also help you calculate the future value of your ordinary annuity. An annuity due is an annuity where the payments are made at the beginning of each time period; for an ordinary annuity, payments are made at the end of the time period. An annuity table cannot be used for non-discrete interest rates and time periods. Although annuity tables are not as precise as annuity calculators or spreadsheets, the benefit of using an annuity table is the ease of calculating the present value of your annuity. An annuity table is a tool that simplifies the calculation of the present value of an annuity. Also referred to as a “present value table,” an annuity table contains the present value interest factor of an annuity , which you then multiply by your recurring payment amount to get the present value of your annuity.

## Calculating The Interest Rate

Try our calculator and see what selling your annuity or structured settlement could get you in cash today. The present value interest factor of annuity is a factor that can be used to calculate the present value of a series of annuities. There is a separate table for the present value of an annuity due, and it will give you the correct factor based on the second formula. Using the same example of five \$1,000 payments made over a period of five years, here is how a present value calculation would look. It shows that \$4,329.58, invested at 5% interest, would be sufficient to produce those five \$1,000 payments. Learn more about how you can improve payment processing at your business today.

Based on the time value of money, the present value of your annuity is not equal to the accumulated value of the contract. This is because the payments you are scheduled to receive at a future date are actually worth less than the same amount in your bank account today. A whole life annuity due requires annuity payments at the beginning of each monthly, quarterly, or annual period, as opposed to at the end of the period.

This example is an easy calculation because we’re dealing with simple round numbers and only one payment period. But when you’re calculating multiple payments over time, it can get a bit more complicated. The time value of money states that a dollar today is worth more than it will be at any point in the future. It makes sense when you consider that every dollar has earning potential because it can be invested with the expectation of a return. So, if you have \$1,000 right now, and you put it in a high-yield savings account with a 1 percent annual percentage yield , at the end of a year, you will have \$1,010.

## Examples: Using Microsoft Office Excel Or Openoffice Calc For Calculating Present Value And Future Value Of Investments

Have you ever had to make a series of fixed payments over a set period of time? If so, you’re probably already familiar with the concept of annuities, even if you’re not so clued up on the terminology. Simply put, annuities are recurring or ongoing payments over a period of time, like rent or payments for a car. There are a couple of different ways that you can measure the cost or value of these annuities. Find out everything you need to know about calculating the present value of an annuity and the future value of an annuity with our helpful guide. One can also determine the future value of a series of investments using the respective annuity table. An annuity table calculates the present value of an annuity using a formula that applies a discount rate to future payments.

The factor is determined by the the interest rate and the number of periods in which payments will be made . In an annuity table, the number of periods is commonly depicted down the left column.

An annuity table provides a factor, based on time, and a discount rate by which an annuity payment can be multiplied to determine its present value. For example, an annuity table could be used to calculate the present value of an annuity that paid \$10,000 a year for 15 years if the interest rate is expected to be 3%. In corporate finance, a discount rate is the rate of return used to discount future cash flows back to their present value. This rate is often a company’s Weighted Average Cost of Capital , required rate of return, or the hurdle rate that investors expect to earn relative to the risk of the investment. A lottery winner could use an annuity table to determine whether it makes more financial sense to take his lottery winnings as a lump-sum payment today or as a series of payments over many years. More commonly, annuities are a type of investment used to provide individuals with a steady income in retirement. Behind every table, calculator, and piece of software, are the mathematical formulas needed to compute present value amounts, interest rates, number of periods, payment amounts, and other future value amounts.

When a business wants to make an investment, one of the main factors in determining whether the investment should be made is to consider its return on investment. Commonly, not only will cash flows be uneven, but some of the cash flows will be received and some will be paid out. Therefore, there are certain formulas to compute the present value and future value of annuities. An annuity table aids in finding out the present and future values of a sequence of payments made or received at regular intervals. The payments received from an annuity are reported as income, and the amount of tax to be paid depends on the product. In the PVOA formula, the present value interest factor of an annuity is the part of the equation that is written as and multiplied by the payment amount. Therefore, if you consult an annuity table, you can easily find the PVIFA by identifying the intersection of the number of payments on the vertical axis and the interest rate on the horizontal axis.

## Example: Calculating Monthly Mortgage Payments

When payments are distributed at the beginning of a period, the annuity is referred to as an annuity due. Annuity due payments typically apply to expenses such as rent or car leases where payments are made on the first of the month. Similarly, the formula for calculating the present value of an annuity due takes into account the fact that payments are made at the beginning rather than the end of each period. The present value of an annuity is the present value of equally spaced payments in the future. The intersection of the number of payments and the discount rate presents a factor that is multiplied by the value of payments, providing the present value of the annuity. Depending upon the numbers you’re working with and how accurate you want to be, an annuity table is a simple and convenient way to calculate the present value of an ordinary annuity. When the payments are fixed, the present value interest factor of an annuity — these are the values that correspond to the intersection of the number of payments remaining and the interest rate — can be simplified.