Work out an indexed annuity credit by hand with your own contract terms

Every indexed annuity statement reports a number, "interest credited," that comes from a short piece of arithmetic. The arithmetic is not hard, but the contract describes it in dense language, and the result often differs from what the index itself did. If you can repeat the calculation with the figures on your own contract, you can check the statement, understand why a good market year paid less than you hoped, and compare one product with another without relying on someone's summary.

This worksheet walks through the calculation with round numbers I made up for the purpose. None of the terms below is any company's real cap or rate, and the index levels are not a forecast. When you reach the blanks, replace each figure with the one from your own contract.

What you need from your contract

Before any arithmetic, collect eight items. They are usually on the data page, in the section on crediting, or in a separate rate sheet or supplement that the contract refers to. If you cannot find one of them, that is a question for the company, and the answer should come in writing.

1. The index. Which one (for example a large-company stock index or a proprietary index built by a bank) and whether it is a price index or a total-return index. A price index leaves out dividends.
2. The crediting method. The rule for turning index movement into interest. The most common is annual point-to-point, which compares the index on two dates a year apart. The other common types are monthly sum, monthly average and multi-year point-to-point. See index crediting method for the family of designs.
3. The measurement dates. Usually the contract anniversary.
4. The cap. The most the contract will credit for the period.
5. The participation rate. The share of the index gain you receive.
6. The spread, margin or asset fee. A percentage subtracted from the index gain before the credit.
7. The floor. The lowest credit, usually 0%.
8. Which of these the company can change, and when. Caps, participation rates and spreads are frequently reset each year; the contract states the minimums or maximums.

Not every contract uses all three of cap, participation and spread. Many use one or two. The worksheet treats each separately, then shows what happens when they are combined.

The seven steps

Here is the full routine for the common annual point-to-point method.

1. Write down the index value at the start of the period (the last anniversary).
2. Write down the index value at the end of the period (this anniversary).
3. Compute the index change: (end − start) ÷ start. Express it as a percentage.
4. Apply participation: multiply the change by the participation rate, if there is one.
5. Apply the spread: subtract it, if there is one.
6. Apply the cap: if the result is above the cap, use the cap.
7. Apply the floor: if the result is below the floor, use the floor. Then multiply the beginning account value by the result to get the dollar credit.

The order of steps 4 to 6 differs among contracts. Some apply participation and then the cap; others use a spread without a participation rate. The contract says which. The examples below follow the order stated for each one.

Worked examples

Example 1: a cap

Say the contract's terms are: annual point-to-point, cap 6%, floor 0%, no participation rate and no spread. The account value at the start of the year is $100,000. The index is 4,000 at the start and 4,360 at the end.

• Step 3: (4,360 − 4,000) ÷ 4,000 = 360 ÷ 4,000 = 0.09, or 9%.
• Step 6: 9% is above the 6% cap, so the credit is 6%.
• Step 7: 6% is above the 0% floor. Dollar credit: $100,000 × 0.06 = $6,000.

The new account value is $106,000. The index rose 9%, and you were credited 6%. The other 3% is the price of the floor: the company is paying for the downside protection partly by keeping some of the upside.

Example 2: a participation rate

Now the terms are: annual point-to-point, participation rate 50%, no cap, no spread, floor 0%. Same index levels, same $100,000.

• Step 3: 9%.
• Step 4: 9% × 0.50 = 4.5%.
• Step 7: dollar credit is $100,000 × 0.045 = $4,500.

The account value is $104,500. A participation rate gives a proportional share of whatever the index does. In a year when the index rises 20%, a 50% participation rate would credit 10%, where the 6% cap above would still credit 6%. In a year when the index rises 5%, the 50% rate credits 2.5% while the cap contract credits the full 5%. Neither design is better in every year; the right comparison depends on the range of markets you expect, which nobody knows.

Example 3: a spread

Terms: annual point-to-point, spread 2%, no cap, no participation rate, floor 0%.

• Step 3: 9%.
• Step 5: 9% − 2% = 7%.
• Step 7: dollar credit is $100,000 × 0.07 = $7,000.

Account value $107,000. A spread is subtracted from every gain, so it matters most in small up years. Suppose the index rose only 1.5% in a year: 1.5% − 2% is negative, so the floor applies and the credit is 0%. The spread consumed the whole gain.

Example 4: combining participation and a cap

Terms: participation 80%, cap 6%, floor 0%, participation applied before the cap.

• Step 3: 9%.
• Step 4: 9% × 0.80 = 7.2%.
• Step 6: 7.2% is above the 6% cap, so the credit is 6%.

When both are present, the cap often does the work in strong years and the participation rate in moderate ones. With a 5% index gain, step 4 gives 4%, under the cap, so the credit is 4%.

Example 5: a down year

Use the cap contract from example 1 for a second year. The index starts the year at 4,360 and ends at 4,142.

• Step 3: (4,142 − 4,360) ÷ 4,360 = −218 ÷ 4,360 = −0.05, or −5%.
• Step 7: the result is below the floor, so the credit is 0%.

The account stays at $106,000. This is the feature that defines the product: the index fell 5% and the account did not fall. It is also worth noticing what the floor does not do. It prevents a loss from index movement. It does not stop charges for riders from being deducted, and it does not restore the 3% you gave up in year one.

Putting years together

Continue the cap contract for a third year with the index moving from 4,142 to 4,349.1, a gain of 5%. Under annual point-to-point crediting with the 6% cap, the 5% gain is under the cap, so the credit is 5%.

Three years of the index took it from 4,000 to 4,349.1, a rise of 8.73%. The contract account grew 11.3%. In this particular path, with a loss in the middle, the floor helped enough to leave the contract ahead of a plain price-index investment. In a path with three rising years, say +9%, +5% and +9% (compounding to about 24.8%), the cap contract would credit 6%, 5% and 6%, about 18.0% in all, and the index would be well ahead. Whether a contract outperforms the index depends on the order and size of the years, which is the reason to treat any illustration as one of many possible paths. The same example under the participation-rate terms gives $107,112.50 and under the spread terms $110,210, both from the same index path.

A monthly example, to show where caps bite

A monthly sum design is built differently. The contract measures the index change each month, caps each month's gain at the monthly cap, leaves each month's loss uncapped, adds up the twelve results and applies the floor to the total. Say the monthly cap is 2%, and the index changes by +3, −1, +2.5, +4, −2, +1, +3, −3, +2, +1, −4 and +2 percent in the twelve months.

• Capped monthly results: +2, −1, +2, +2, −2, +1, +2, −3, +2, +1, −4, +2.
• Sum: 4%.
• Floor: 4% is above zero, so the credit is 4%.

The uncapped sum of the same months is 8.5%. The monthly design cut off the big up-months while counting every down-month in full, which is why this method can credit a modest amount in a year that looked strong on the index chart. This is also one reason it is hard to judge a contract from its cap alone: the cap's meaning depends on the method.

The same terms across many index results

One way to see how the designs differ is to hold the terms fixed and vary the index. The table uses the four sets of terms from the examples above (a 6% cap; a 50% participation rate; a 2% spread; an 80% participation rate with a 6% cap), all with a 0% floor, applied to a single year of annual point-to-point crediting.

Read across a row and the point is plain. The cap is best in small and moderate years and flat in big ones. The participation rate trails in small years and keeps pace in big ones. The spread behaves like a flat deduction, so it is the most generous in large years and the least in small ones. No design wins everywhere, and a contract that pairs a favorable-looking number (a high participation rate, say) with another limit (a low cap) may do neither well. Because the company sets these numbers to fit what it spends on the options that fund the credits, a generous figure on one line often comes with a tighter figure somewhere else.

A multi-year example

Some contracts measure over a longer term, such as six years, and credit once at the end. Say the terms are a participation rate of 70% over a six-year term, a floor of 0% and no cap, on $100,000. The index starts at 4,000.

• If it ends the term at 5,200, the change is (5,200 − 4,000) ÷ 4,000 = 30%. Participation: 30% × 0.70 = 21%. Credit: $21,000, for a value of $121,000.
• If it ends at 3,600, the change is −10%, the floor applies and the credit is 0%.

Notice what is missing. The 21% is the total for six years, not a yearly figure. Spread over six years, it is about 3.2% a year compounded, since 1.21 raised to the power of one-sixth is about 1.0323. The index itself rose 30%, or about 4.5% a year compounded, and excluded dividends. When you see a multi-year credit, divide it down to an annual equivalent before comparing it with anything else.

Checking a real statement

When you receive an anniversary statement, find these lines, which carry most of what you need for the worksheet: beginning value, index values on the start and end dates, the rate or factor applied (cap, participation, spread), interest credited, charges, withdrawals and the ending value. If the statement lists only the credited percentage, call the company and ask for the index values and the calculation. The walkthrough in reading your annual annuity statement line by line covers the other lines of a statement. If the contract's data page is unfamiliar, how to read an annuity contract page by page before you sign shows where each term lives.

Two adjustments many statements apply

• Charges. If the contract has a rider with a charge, the charge is subtracted from the account value, usually on the anniversary, and the floor on the index credit does not stop it. Say a rider charge of 1% of the account value applied at the end of year two in the example: 1% of $106,000 is $1,060, and the account would fall to $104,940 despite the 0% credit. The charge may be based on a benefit base instead, as explained in annuity fees, explained.
• Early withdrawals and surrender. Many contracts credit index interest only on the anniversary, so a full withdrawal 11 months into the year may receive no credit for that year, or only a portion. Partial withdrawals may be treated in different ways. Surrender charges and any adjustment apply separately; see annuity surrender charges and free withdrawals.

Your worksheet

Make a copy of this table on paper and fill it in from your contract and your latest anniversary statement.

Compare your result with the statement. If the two match, you understand the mechanics. If they differ, the likely causes are the following, in rough order of frequency:

1. The statement used different measurement dates than you assumed.
2. The cap or participation rate on the statement is the renewed rate for the new term, not the one at purchase.
3. The order of the steps is different from the order you applied.
4. A charge, a withdrawal or a partial-period rule changed the base.
5. The index in the contract is a different index, or a total-return version, from the one you looked up.

Ask the company to send the calculation in writing. A properly run contract can show it.

What the arithmetic cannot tell you

Doing the calculation shows you what a past year paid. It does not show you what the next year will pay, because the cap, participation rate and spread for future periods are set by the company within the limits in the contract. The gap between today's rate and the contract's guaranteed minimum is the room the company has to reduce it. The post on declared rates and non-guaranteed elements in annuity contracts sorts each term into guaranteed and changeable, and the claims commonly made in sales conversations are tested in eight claims about indexed annuity returns, tested one at a time. For the overall picture of the product, read fixed indexed annuities: caps, participation rates and trade-offs. For an unbiased check on your own contract and tax picture, a fee-only planner can verify the statement with you.

Key takeaways

• The credit comes from a repeatable sequence: index change, then participation, spread, cap and floor in the order the contract specifies.
• A cap, a participation rate and a spread each reduce the upside differently, so equal-looking terms can produce very different credits in strong and in modest years.
• The 0% floor protects against index losses but not against rider charges, surrender charges or the upside you gave up in good years.
• Monthly and multi-year designs change the arithmetic, so confirm the crediting method before comparing two caps.
• Rates for future periods can be reset within the contract's limits, so use the worksheet to verify statements and compare products, not to forecast.