Calculating Present and Future Value of Annuities

An annuity is a series of payments made at regular intervals. Generally, the term is used to describe an investment product commonly sold by insurance companies and other financial service providers.

Annuities provide a steady stream of income paid out at regular intervals in exchange for a lump sum payment or a series of payments made over a period of time. Like 401(k)s, annuities provide tax-deferred investment growth for retirement income.

How to calculate the present value of an annuity

The present value of an annuity refers to the current value of future annuity payments. Understanding an annuity's present value can help you make informed decisions when choosing between accepting a lump sum payment or a fixed annuity.

The following formula is used to calculate an annuity's present value. Keep in mind this is the formula for the present value of an ordinary annuity. An ordinary annuity is paid at the end of a predetermined time period.

P = PMT x [1 – [ (1 / 1+r)^n] / r]

• P: The annuity stream's present value

• PMT: The dollar amount of each payment

• r: The interest or discount rate

• n: The total number of payment occurrences

For example, let’s say you’re offered an annuity product that will give you monthly payments of $10,000 for the next 10 years in exchange for a one-time $1 million lump sum payment. This might seem like a good deal. After all, $10,000 multiplied by 120 months will yield a final payout of $1,200,000, which is $200,000 more than the lump sum payment.

However, we could also invest that $1 million in the stock market, generating additional income since inflation will eat away at each subsequent payment. Assuming an annual interest rate of 10%, let's use the present value of an annuity formula to see the expected current value of the annuity payment.

$756,712 = $10,000 x [1 – [ (1 / 1+0.1)^120] / 0.1]

In this case, the present value of our annuity payment comes to just under three-quarters of a million dollars, making the lump sum payment a clear winner. What increases the present value of an annuity? You can increase the payment amount, the interest rate or the payment frequency to raise an annuity's present value.

You can also use the present value of an annuity due formula to calculate the present value of an annuity paid out or collected at the beginning of a predetermined time period.

PV= PMT x [(1 – (1 / (1 + r) ^ n))/ r] x (1 + r)

• PV: The annuity's present value

• PMT: The amount of each payment denominated in dollars

• r: The interest or discount rate

• n: The total number of payment occurrences

How to calculate the future value of an annuity

The future value of an annuity helps individuals project how much a series of payments will be worth at a certain point in the future. You can use the following formula to calculate the future value of an annuity:

​P=PMT×(((1+r)n−1)/r)​

• P: The annuity stream's future value

• PMT: The amount of each payment denominated in dollars

• r: The interest or discount rate

• n: The total number of payment occurrences

When you sit down to plan for retirement, more likely than not, you will calculate the future value of an annuity. For example, if you can afford to invest $1,000 a month and want to retire in 15 years, you will have $1,969,000 at the end of the interval, assuming an interest rate of 10%.

1,969,000=$1,000x(((1+0.1)180-1)/0.1)

If you aim to save $2 million by retirement, then you're right on track. If you'd like to have a little more in your bank account or if you'd like to hedge your bets with a lower interest rate, you can play with the formula by entering different numbers until you arrive at a figure you're comfortable with.

Present vs. future value of an annuity: what's the difference?

The present value of an annuity allows you to accurately value the present worth of a series of annuity payments. You can use this information to come up with a cash equivalent for an annuity, which in turn helps you buy and sell annuities. This information can also help when comparing lump sum payments and future annuities.

Meanwhile, use the future value of an annuity formula to guide your long-term goal setting. If you’re planning for retirement, for example, calculating the future value of an annuity can help you make accurate projections for the future.

The main types of annuities

The following section covers the most important annuity types. We've broken down each type into subgroups according to key characteristics. Keep in mind as you go through this list that an annuity will have characteristics from multiple categories.

For example, you can purchase a variable annuity that is also a deferred annuity, which uses an annuity's due payment schedule. As you learn more, mix and match the different annuity types to come up with the annuity that best suits you.

Based on annuity growth

The following annuity types are defined by the amount of volatility they can experience. Annuity types with greater volatility have the potential to earn more money, but those gains can also vanish due to market fluctuations. Lower volatility offers protection against a down market, but it also caps growth during hot markets.

Fixed

A fixed annuity guarantees a specified rate of return in exchange for a lump sum of money or periodic payments. Buyers of fixed annuities gain stability at the expense of potentially higher gains.

Many older Americans purchase fixed annuities to buffer against bad years in retirement. While most younger investors are better off with more dynamic investments that yield higher rates over the long run, the calculus shifts when retirement begins and the timeline to recover from a bad market shrinks.

Fixed annuities can offer tax-deferred growth. Some annuities can be passed on to the beneficiary's heirs under certain circumstances, such as when the beneficiary dies before the first payment.

Fixed index

Fixed index annuities track an underlying stock index such as the S&P 500 or the Russel 2000. As with fixed annuities, fixed index annuities are popular with retirees. A fixed index annuity provides more variability than a fixed annuity while still protecting the beneficiary against volatile markets. However, the stipulations established in your contract limit both your earnings and loss potential.

Fixed index annuities accomplish this by providing a floor and a ceiling for your investment returns. For example, a contract may state that 0% marks the lowest return you can get on your investment. Even if the market dips 20%, you'll just break even. On the flip side, your contract might limit your investment gains to 5%. Even if the market shoots up by 20%, you'll only receive a 5% gain.

Variable

Variable annuities allow you to save for retirement by investing in a portfolio of subaccounts. Subaccounts function similarly to mutual funds. However, you cannot easily research subaccount performance through a fund tracker. Variable annuities offer the potential for greater gains compared to fixed indexes and fixed annuities. However, this annuity type does not limit losses, which may deter some investors.

Based on the time of payout

You can broadly divide annuities into two categories based on when you begin receiving payments.

Immediate

Annuities that offer immediate payouts convert a one-time payment (sometimes known as a single premium annuity) into an ongoing payment stream. Payments last for a predetermined period of time, typically between five years and the buyer's death. Immediate annuities best fit the needs of individuals close to retirement, with payments starting within the first year after one-time payment is completed.

Deferred

Deferred annuities function more like 401(k)s in that policyholders make regular premium contributions over a long period before they start receiving payments. For example, a 50-year-old individual may make annual payments on a deferred annuity for 15 years. At 65, the individual will start to receive payment benefits. Since annuities are tax-deffered, they’lll only have to pay taxes on the payouts as received.

Based on the payment period

Annuities can be divided into two further subcategories based on when the payment occurs.

Ordinary annuities

Ordinary annuities are paid at the end of a predetermined period. This period could be weekly, monthly, quarterly, annually or at any other regular time interval.

Annuities due

Annuities due are paid at the beginning of a predetermined period.

Because the time value of money dictates that money in the future is less valuable than the same amount of money in the present, ordinary annuities may be less desirable than annuities due when receiving payments. Additionally, when making payments, ordinary annuities may be more desirable than annuities due.

Multi-year guaranteed annuity potential

This type of annuity operates much like a CD. Once you sign a contract with an insurance provider, you deposit a premium on which the insurance company pays interest regularly at a predetermined rate. After the contract completes, you receive both the principal and the accrued interest.

Most contracts last somewhere between three to ten years. While the contract is in force, you may not withdraw your money unless you pay a penalty or "surrender fee." Some contracts have exceptions allowing you to withdraw partial sums at fixed intervals. You may also be able to take out a loan using your annuity as collateral.

Lifetime annuities

Many insurance companies sell lifetime annuities to retirement-age individuals. As the name suggests, lifetime annuities last until the buyer's death. Sometimes, lifetime annuities may be transferred to the buyer's spouse upon the annuity holder's death.

Insurance companies calculate lifetime annuity payment schedules using complex actuarial tables. Lifetime annuities remain popular with individuals who value security. Single premium lifetime annuities can be purchased with a single lump sum.

Fixed period annuities

Fixed-period annuities provide annuity payments for a predetermined period, such as 10 years. After the period expires, the annuity stops paying out. The annuity will also stop upon the beneficiary's death unless the contract allows them to transfer the annuity to an heir. Unlike lifetime annuities there's a risk that you may outlive your fixed annuity, leaving you without income in your old age.

The importance of annuity valuation

Calculating the value of an annuity can help you make informed decisions about major life changes, such as when you can afford to retire or which annuity product to buy. Whether you use an annuity formula or an annuity calculator, proper valuation can help you project future cash flow and estimate the payments you need to make to meet your financial goals.

Determine the worth of your investments

When determining the present value of an annuity, you should take the type of annuity into account. Remember, annuities can belong to multiple categories, and each category can influence the annuity's total value. For example, deferred annuities won't pay out for years, while immediate annuities begin to pay out as soon as the policy's in force. Keep in mind the time value of money, and be sure to use the correct formula when calculating your annuity investment.