An annuity is an investment that purchases a stream of income. Both the principal, AKA invested capital, and interest are paid back in a fixed payment over a period of time. A “term annuity” makes its payments for the period specified at purchase. A “life annuity” combines an investment with the mathematics of life insurance to make equal payments over an individual’s life span.

## What is an Annuity?

An annuity is a contract that is issued by a financial institution. It repays the invested capital over a period of time plus interest on the outstanding balance. Consider the purchase of a \$100,000 annuity. The investor or “annuitant” gives \$100,000 to the financial institution. In return, the investor receives a promise from the institution to pay a defined stream of income over a specified period. Annuities are always based on a specified interest rate that determines the interest portion of the payment.

## Principle of Annuities

For our example, let’s assume a 6% interest rate. If none of the principal were paid during the term of the investment, we would receive \$6,000 per year until repayment of the principal of \$100,000 at maturity. Sounds an awful lot like a bond, which it is. Now let’s decide to repay a certain amount of the principal each year. As with a mortgage, this is known as the “amortization” of the principal. For simplicity’s sake, let’s assume that the principal is repaid evenly over the term of the annuity. In this case let’s assume 10 years. This is known as “straight line” amortization. At the end of the first year, we would have an interest payment of \$6,000 based on our starting principal of \$100,000 and a principal payment of \$10,000 or 1/10 of the original principal. This would mean a total payment of \$16,000 (\$6,000 interest plus \$10,000 principal). Note that this total payment of principal and interest is much larger than the \$6,000 interest only payment on a bond. This higher payment level is the major reason that annuities exist.

Think what happens in the second year. Since we start with only \$90,000 outstanding (remembering that we already paid \$10,000 of the original principal at the end of the first year), we only get 6% on \$90,000 or \$5,400 in interest. When we combine this \$5,400 with the straight line principal payment of \$10,000 from the original \$100,000, we get a total payment at the end of the second year of \$15,400. This is \$600 less than our first year payment of \$6,000 because of the lower outstanding principal.

In the third year we get a payment of \$14,800. This is comprised of \$10,000 in original principal but only \$4,800 in interest, since at the end of the second year we only have \$80,000 of original principal outstanding. With this “straight line” amortization of principal, the principal repayment is constant at \$10,000 but the interest decreases with the declining outstanding principal on which it is calculated over time. At the end of the 10th or last year of the term, we have an interest payment of only \$600 since we ended the 9th year of the term with only \$10,000 of original principal outstanding. This combines with the final \$10,000 payment of principal to make the final payment of \$10,600.

In our example above, we received our entire principal back over the term of our annuity with interest on the outstanding balance. We can see that the interest rate of 6% set the level of the interest payment in each year. If the rate were higher, the interest payment and total payment would have been higher. The reverse is true as well. A lower interest rate would have lowered the interest payment and hence the total payment.

We have one problem. Our payment changes over the term of the annuity with our “straight line” amortization. We start with a first year payment of \$16,000. The payment drops to \$15,400 in the second year, \$14,800 in the third year and so on until the final payment of \$10,600 in the last year of the 10-year term.

The way around this problem is to find a principal payment pattern that keeps the total overall payment the same. This is called “blended amortization” and works exactly the same way as a mortgage, except in reverse. Think about it for a minute. We could start with very small principal payments at first, when the interest payment is large because of the large outstanding principal balance and then have larger principal payments near the end of the term when the interest payment is smaller. Mathematically, there is a payment for every interest rate, term, and principal amount that maintains a blended level payment of principal and interest, and pays back all of the principal over the term. Thankfully, we have calculators and computer spread sheets to perform this calculation. In the case of our example, it is \$13,586.80. This is the level payment of “blended principal and interest” which pays off the outstanding principal exactly over the term.

To develop a better understanding of the mathematics of amortization, try the finance functions of your calculator or spreadsheet. Building a spreadsheet to see how the principal is paid down over time is a particularly good way to see this better.

### A Life Annuity

A “life annuity” combines the repayment of principal of an annuity with mathematics of life insurance. Using “actuarial mathematics” – the insurance statistics of life expectancy – an actuary substitutes the average life expectancy of a group of insured people for the term of the annuity. Let’s say you are retiring at 65 and look at purchasing a life annuity with the \$100,000 proceeds of your RRSP or proceeds of your defined contribution pension plan. The good people of “This is Your Life Insurance Co.” tell you that they will provide a quote. What they do is take the average life expectancy of someone your age and assume a payout over this period. Let’s say that their statistics or “tables” expect that people your age will live on average for 20 years or 85 years old. This is the term that they use for their calculations on the term for your annuity.

As in all statistics, only only a few people in the insured group will attain an average life expectancy. Most people in the group will live slightly longer or slightly shorter than the average. Fewer will live a fair bit longer or shorter than average. A few “outliers” will live for a very short time or a very long time. But, “on average”, the members of the group who live longer will cancel out those who live shorter lives. From This is Your Life Insurance Co.’s, our annuity issuer, point of view those living longer and receiving more money will be offset by those living shorter lives and receiving less.

### Actuary Tables

The statistics of life expectancy are morbid (in fact, actuaries use Morbidity and Mortality Tables), but they tell us a lot about how much we will get from a life annuity. An insurance company, like This is Your Life , uses standard statistics for its insurance risk underwriting. A less healthy person will live a shorter period than a healthy person and therefore will get a higher payment over the statistically shorter life-span. A female lives longer and will therefore get a lower payment because of her statistically longer life expectancy and therefore term, than a male of the same age. An annuity that continues to pay to the survivor of a married couple, “joint and survivor”, will have a lower payment due to the likelihood, statistically, that one of two people will live longer than one individual.

## Are annuities good investments?

The principle of an annuity is sometimes hard to grasp, but it could be an important consideration for a source of retirement income. As in all things financial, the best way to assess an annuity is to examine the cash flows. Higher interest rates make for higher payments. More investment opportunities make for higher yields for issuers to fund annuities. Can the issuer invest, after expenses, better than the investor or purchaser? It’s likely that Great-great Aunt Cecily won’t be spending a lot of time at the nursing home ‘running’ her own money, so maybe even the conservative folks at This is Your Life Insurance Co. might be a reasonable alternative. What’s the investment need for? If there’s no need to have anything left over for the parasitic relatives, Aunt Cecily might consider a life annuity which would expire when she did, while offering a much higher income along the way.

As in all things financial, do your research. Now that you can answer the question ‘what is an annuity’ you can take a look at what’s out there. Consider your needs. Consult some reputable professionals in the field. Keep your head up!

6 years ago