Perpetuity vs Annuity – Difference Between the Two with Examples and Formulas

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As a general rule, money offers a time value. If you have $1 today, then it will be more valuable now than it will be 12 months from now. The value of money declines because of the act of inflation. By determining what the time value of money will be in the future, it becomes possible to determine what the value of a fixed financial asset will be.

Two methods that are used to create wealth for a future retirement or other financial need are perpetuities and annuities.

An annuity is a series of cash flows, which are provided in a fixed amount under most plans, that is received by an individual at a regular interval. This creates the replication of income, as if one were employed, on a payment schedule which meets personal financial needs.

Annuities can be paid out with several different interval schedules, depending upon the structure of the plan and the needs of the individual. Everything from monthly to annual annuity payments are considered common.

A perpetuity is like an annuity except for one important difference. With an annuity, the money will eventually run out because there is a scheduled end to the payment schedule. With a perpetuity, the payments continue on the same schedule infinitely.

The Definition of an Annuity

An annuity is based on a large cash deposit that is made several years before the cash flows are required by an individual. Many annuities have a minimum initial contribution amount of $100,000 to $250,000. Some may require even more.

For the standard annuity, there are several structures from which to choose. Some offer a fixed rate of return, while others offer a variable rate.

To understand what the maturity value of an annuity will be, it is important to use this formula.

MV = X [1+R]n – 1 over R.

MV equals the maturity value of the annuity. X is the amount of the annuity. N is the number of years that are part of the annuity agreement, while R is the rate of return.

The Definition of a Perpetuity

The term “perpetuity” is combination of the two words “perpetual annuity.” It provides a constant stream of cash over the years without a fixed end date.

As with other annuities, a perpetuity is started with an initial funding of principal. Once the account is established, the schedule for cash flows will start. The difference here is that the cash flows are interest payments that are generated from the initial deposit.

With a perpetuity, you don’t have a fixed ending date because you are not digging into the principal amount of the initial deposit. Your income stream is the interest that is generated from the investments that are made with that principle amount.

You have two options to consider when looking at a perpetuity. It can either be a constant amount, where the return is the same every year, or it can be a growing structure. With a growing perpetuity, you would receive an increased return, at a uniform rate, for the life of the account.

To determine the present value of a constant perpetuity, your formula is simple: it is C/R. C equals the cash flow, which is your interest or dividends earned from the principal deposit. R is the interest rate that is expected or dictated by the perpetuity agreement.

For a growing perpetuity, the formula is only slightly more complicated. It is C over R-G.

C and R represent the same elements in this formula as they do for the constant perpetuity. G is the growth rate that is expected or dictated by the agreement which governs the account.

What Are the Benefits of an Annuity?

Choosing an annuity product, whether it is a standard annuity or a perpetuity, is that you are able to set aside a lot more money for retirement compared to other plans. You still benefit from being able to defer paying taxes on the amount that is saved in the annuity, even though the annual contribution caps are not in place like they are with a 401k, IRA, or 457 deferred plan.

That can be very useful for those who are approaching retirement age and need some extra money to be stashed away without the threat of taxes now.As with the other tax-advantaged plans, with an annuity or perpetuity, you would pay income taxes on the distributions you take from the plan when you need to have cash.

Another advantage of choosing an annuity (or perpetuity) is that the money you’re investing will compound each year without a threat of taxation. All the money that you have growing within this type of account will grow tax free until you choose to take a distribution. You may have plan administration fees and trading fees to pay (along with other fees and costs), but taxes aren’t administered until you take money out of the account.

With an annuity, you do have the option to cash out with a lump-sum payment. If you choose a perpetuity, you don’t really have that option. The whole point of the perpetuity is that you setup a lifetime source of income once you start taking interest distributions from the amount that was saved.

If you do take out an annuity with a lump-sum cash payment, that means you’ll be responsible for the income taxes on the amount you take during that tax year. That can create a severe tax penalty for some households.

Let’s say you have set up a $250,000 annuity on an income of $60,000 per year. You wait until the maturity date to close out the annuity, then take everything in a lump-sum payment. The amount you deposited grew to $325,000.

Instead of being responsible for $60,000 in income taxes, less deductions and credits, you would now be responsible for $325,000 in income taxes in the tax year where you took the distribution.

For that reason, many choose to take guaranteed payments from their annuity over a specific length of time. You can even set it up to provide payments for the rest of your life, ensuring that there is a steady income stream to support your needs now and well into the future.

A Word of Caution with Annuities

An annuity or perpetuity is designed to be a supplemental form of income. This retirement option works best when you use it in conjunction with your pension plan, 401k plan, IRA, and Social Security checks.

By having multiple income streams at retirement, you’ll be able to enjoy the time away from work without worrying about your finances.

As with any financial decision, it is important to discuss the pros and cons of annuities and perpetuities with your professional advisors before making a final decision.