What is Perpetuity and Annuity? Comparison Chart of 9 Areas

Your vision is to understand a little more about investments.

You would like to understand financial terms, perpetuity, and annuity to start with. What do these mean and are you missing out by not knowing what they are?

You’re not necessarily missing out, however, if you want to learn more about investing, and as you move closer to retirement, which we all are, there are some terms you should be familiar with if you aren’t already. This comparison and contrast chart and the examples break down perpetuity and annuity to make it easy to understand.

Comparison chart of perpetuity and annuity

How to calculate a perpetuity

Let’s use an example of a bond that is going to pay for an infinite time. The bond will pay $200 every year and the interest or discount rate is 5%.

PV = $200 / .05

PV = $4,000

If you have a bond that pays $200 each year infinitely at 5%, the present value of the perpetuity is $4,000, which would be the price of the bond.

Why would you purchase an annuity?

1. The stock market has too much up and down for you
2. You like to know how much interest you will make
3. You like stability and knowing you can predict the income you will have
4. You don’t qualify for life insurance
5. You worry about long-term care and want to have that covered.

How to calculate an annuity

Let’s use an example of someone who is likely to purchase an annuity. They want to move $20,000 to an annuity with a .5% monthly interest rate for 10 years. We are going to switch this formula around to make this a more real-life example given our scenario. We want to find the value of each payment.

P = PV X (r / (1-(1+r) ^-n))

P = $20,000 × (0.005 / (1−(1.005)^−120))

P = $220

Now, look at $20,000 vs. $220 * 12 months in a year * 10 = $26,400.

By purchasing the annuity, you are up $6,400 over 10 years. You can see this is potentially safer than stocks, but with that interest rate, you may have just kept up with inflation. It’s still better than letting the money sit.

In summary, when you hear the terms perpetuity and annuity, you should be comfortable in knowing the differences and what it looks like to quickly calculate either one.

Useful references if you want to look further into perpetuity and annuity.

https://www.investopedia.com/ask/answers/060915/what-are-differences-between-annuity-derivation-and-perpetuity-derivation-time-value-money.asp

https://www.investopedia.com/ask/answers/040715/annuity-perpetuity.asp

https://www.wallstreetmojo.com/annuity-vs-perpetuity/

https://www.goodfinancialcents.com/why-you-shouldnt-buy-annuity-and-5-real-life-scenarios-when-you-should/

https://www.omnicalculator.com/finance/perpetuity#perpetuity-in-real-life-examples

This article focused on the differences, however, there are more types of annuities, this article has more information on those.

https://www.thrivent.com/posts/annuities/the-4-types-of-annuities-which-is-right-for-you.html