Can You Predict the Annuity’s Future Value?

An annuity’s future value is the present value of a stream of payments or receipts postponed to a future date at a given interest rate.

## Annuity Value in the Future: Some Background

An annuity consists of a series of payments paid at regular intervals. Each of these installments includes interest that is compounded. Annuities are frequently referred to as “rents” since they function similarly to the monthly payment of a lease.

Payments from an annuity can be made at the start or finish of each interval. An annuity due is one in which payments are made at the start of the term, whereas an ordinary annuity is one in which payments are made at the conclusion of the period.

Ordinary annuities are used for the examples in this article. As a result, the payment is assumed to occur at the conclusion of the period in every article.

## Annuity Examples

Financial and business contexts frequently involve annuities. Annuities include things like rent and mortgage payments. In the context of life insurance, an annuity is a contract that guarantees a series of payments at regular intervals.

## Finding an Annuity’s Future Value

Calculating the annuity’s present value may be more appropriate in some situations, while estimating its future value may be more appropriate in others. First, we’ll break down how to estimate an annuity’s future worth.

All of the annuity’s periodic payments plus interest earned on them is its future worth.

To illustrate how to determine an annuity’s future worth, let’s pretend you put $1 into a savings account at the end of each of the next four years, earning 10% interest compounded annually.

Each dollar’s future value is calculated by applying compound interest at 10% for the specified number of periods. If you deposit $1 at the conclusion of the first period, you’ll get $3 in interest.

Because it was placed at the end of the first period, it will only accrue interest through the end of the fourth period.

Future value = (Factor) x (Principal)

= $1.3310 x $1.00

= $1.3310

Two interest periods on the second payment add up to $1.2100, and one interest period on the third payment adds up to $1.10.

Since we are calculating the future value of the annuity at the conclusion of the fourth period, the final payment made at the end of the fourth year does not generate interest.

This standard annuity’s future value, calculated by adding all payments and compounding them for the correct number of interest periods, comes to $4,6410.

The future value of an annuity can be calculated without resorting to such a table, which is good news. For various time periods and interest rates, we may look up the future value of a single dollar’s worth of an annuity in tables.

In this sense, the table above qualifies. Simply adding up the appropriate components from the compound interest table allows us to construct this table.

When we did the computation on our own, we found that the future value of a $1 annuity after 4 years at 10% compounded annually is $4.6410.

Issues Concerning Annuity Value Projection

The following is a general formula for calculating the value of an annuity in the future, which can be used to a wide range of applications.

Formula

## Annuity Present Value = Factor x Annuity Payments

Two of the three variables can be known in order to determine the third. An annuity’s future value, payment, interest rate, or period length can all be calculated in this way.

Estimating Value in the Future

Let’s say for the next eight years, you put $4,000 into a savings and loan at the end of each year. If your investment returns are 10% per year, how much money will you have after ten years?

This annuity’s expected value in the future is $45,743.56.

## Annuity Present Value = Factor x Annuity Payments

= 11.43589 x $4.000

= $45,743.56

How the Annuity is Calculated

Let’s say you have 15 years to save up $100,000 so you can send your daughter to college.

How much would you need to put away per year for 15 years at a local savings and loan earning 12% in order to have $100,000 by the end of the 15th year?

The following calculations yield a yearly sum of $2,682.42:

Annuity Present Value = Factor x Annuity Payments

## The amount of an annuity payment is calculated as follows:

= $100,000 / 37.27972

= $2,682.42

## Interest Rate Setting

Calculating the required interest rate for an annuity to accrue a certain sum is useful in certain circumstances.

For illustration purposes, let’s say you wish to invest $500 every three months for ten years in order to have $30,200.99 by the end of the tenth year. At what rate of interest must we invest?

You must achieve a 2% quarterly return, or a yearly return of 8%, as calculated below.

Annuity Present Value = Factor x Annuity Payments

Variable = Present Value of Future Annuity Payments

= $30,200.99 / $500

= 60.40198

Given that the annuity is to be paid out every three months, we must scroll down the table to the row corresponding to the fortieth period (10 years x 4). In this instance, it can be found in the 2% range. As a result, the rate of interest is 2% per quarter, or 8% per year.

In certain cases, we have the interest rate but no idea how many periods are involved.

The method we used to calculate the interest rate can also be used to solve these difficulties. After the factor is calculated, it should be used to locate the factor in the corresponding interest column of the annuity table.