Actuarially fair SPIA and DIA price calculator

financial planning

This calculator computes actuarially fair prices for Single Premium Immediate Annuities (SPIAs) and Deferred Income Annuities (DIAs). An annuity is actuarially fair if the price paid for it equals the expected present value of the income stream it provides. This calculator does not provide SPIA or DIA quotes, but it does allow you to ballpark such quotes, and help you decide if a quote you have already received is a good deal.

Quotes need not be actuarially fair. Costs, including sales, marketing, administrative, and bond default costs, profit margins, and taxes all reduce the Money's Worth Ratio (MWR). On the other hand the MWR may increase as a result of insurance companies investing premiums in assets more risky than the assumed bonds.

Source code to the SPIA module is made available in the hope this will lead to feedback and improvement. Files: README.spia, agpl-3.0.txt, spia.py, and fetch_yield_curve.

Annuitants

Sex: Age: years months

Secondary annuitant: Age: years months


Payout when one annuitant is dead: %

Life expectancy




Annuitant life table is Society of Actuaries 2012 Individual Annuity Mortality Basic Table with Projection Scale G2. General population life table is U.S. Social Security Administration Actuarial Study No. 120.

When using the annuitant life table adjust for contract duration by applying actual/expected data.
Long standing annuitants have a higher mortality than recent annuitants. This adjustment has a significant effect at advanced ages. Adjustment based on Society of Actuaries 2005-08 Individual Payout Annuity Experience Report.

When using the adjusted life table enter the additional remaining years of life expected for the primary annuitant: secondary annuitant:
Adjusted life table applies a constant factor to the qx values of the general population life table in order to reproduce the specified additional remaining life expectancy.

Interest rate

Assumed bond type:
For inflation indexed SPIAs the assumed bond type should be inflation indexed TIPS. For constant nominal payout SPIAs the assumed bond type can be either U.S. Treasury or U.S. corporate, depending on how you are likely to invest your safe assets in the absence of SPIAs.
Quote date: Determines interest rate yield curve.
Apply any inflation adjustment every
Inflation indexed and Treasury based SPIAs priced using the daily U.S. Treasury Yield Curves based on secondary market quotes. Corporate SPIAs priced using the U.S. Treasury High Quality Markets (AAA, AA, A) Corporate Bond Yield Curve. The corporate bond yield curve is only produced monthly with a two week delay, so in times of rapidly changing rates the prices for corporate bonds may not be as accurate as desired.

Adjustment to apply to bond interest rate: %
This term enables experimentation with the effect of changes in the interest rate. For instance, enter a negative value like -0.4% when using corporate bonds to account for the effect of bond downgrades and defaults. The value entered is applied across the yield curve.

Payout

Payout frequency:
Period certain of years from first payout within which full periodic payout amounts are guaranteed.
Payouts begin on or after years months from quote date.
Payout values for inflation indexed DIAs are inflation indexed as of the quote date.

Goal

Enter any two of the following three fields and we will compute the missing field:

Premium:
Periodic payout:
Money's Worth Ratio: %
An MWR of 100% signifies an actuarially fair annuity. MWR's in the 90-100% range are typical in the U.S. market.

We will also report the cost of self insuring by buying bonds to cover through the th percentile of life expectancy.