# Life Annuity 101

Written by Lawrence Hii:

What is an annuity?

The basic definition for an annuity is that payments are made at regular intervals. After that, almost anything can occur. From exam FM/2, an annuity is defined to make payments at regular intervals for a predetermined time period. The time period may be 5 years, 10 years or even forever. A perpetuity is an example of payments that last forever. The key is that the number of payments is predetermined at the beginning. However, a life annuity has a different definition for how long payments are made. A life annuity makes payments for as long as you live. Obviously, when a life annuity starts, we don’t know how long we will live. Thus, the number of payments is unknown.

A life annuity is part of the syllabus in EXAM SOA MLC or CAS 3LC (starting Jan. 2014). Many annuities in the market are life annuities. Thus, the distinction between the term “life annuity” and “annuity” is important.

So, how does a life annuity work?

If you purchase a pure life annuity, you will receive payments as long as you remain alive. Here’s an example: Assume you are a 65-year-old male annuitant. Suppose in early January 2013, you invested \$100,000 to purchase a life annuity paying \$500 a month for the rest of your life. This means, you, as the annuitant, will receive \$500 x 12 = \$6,000 per year. Notice this is 6% of your \$100,000 premium. Payments are received for as long as you remain alive. Observe this is a simple level payout where payments are not adjusted for inflation.

Receiving payments for as long as you live sounds great. However, you must understand the risk that you are assuming. What is the risk? The risk is that you will die early and lose all future payments. What does it mean to die early? Assume you live for exactly 16.67 years, calculate how many total payments you’ll receive. You will receive \$6,000 x 16.67 or \$100,000 in total. Notice you only receive your original investment back. For every year, you live beyond age 81.67 (65+16.67), you receive more than your original investment. Thus, if you die before age 81.67, this clearly is a bad investment decision.

Does that mean life annuities are super risky? Depends. The example is a pure life annuity. A pure life annuity does not have any guarantees because a pure life annuity does have significant risk from dying too early. Most life annuities purchased have additional guarantees. The guarantees exist in many forms. One common form is called a certain guarantee period. Consider this example: you will receive \$x per month for at least 10 years or as long as you live, whichever is greater. Thus, if you die before 10 years, you receive payments for 10 years. This payout is called a 10 year certain and life. The name is clear. You receive 10 years of payment for certain. Also, you receive payments for life. For example, if you die after 3 years of payment, your beneficiary will receive the remaining 7 years of payments. If you live for at least 10 years, you receive the same payments for life. Once payments reach 10 years, your beneficiary does not receive any payments after you die.

This seems like a great option. Of course, all options come at a cost. In our example, a pure life annuity paid \$500 per month from an investment of \$100,000. If you choose a 10 year certain and life payout, the monthly payment decreases below \$500. How much below? You can answer that question after studying MLC or 3LC. There are rare past SOA problems that introduce this topic in exam FM/2. You can find an example with a video solution here:

http://youtu.be/t-qf_HW_7vk

Annuities are major topics for actuaries in insurance or investment companies. It is good to have some basic knowledge about annuities.