FAQ 1130: Lifetime Income - How is it calculated?

Problem: How is the Lifetime income shown on the employee statements calculated?

Solution: https://fast.wistia.net/embed/channel/14xhueun3q?wchannelid=14xhueun3q&wvideoid=cnoml3b8iv The "Life only APR" and "100% J&S Rate" fields will store the Annuity Purchase Rates generated by the system when Calculations - Valuation - Plan Totals and Projections for the employee's Single and J&S 100% monthly Lifetime Income annuity amount to be displayed on the Employee statement. APR fields are based on the age of the Employee and the years until they turn age 67 (or their current age if older), the Mortality Table and the Interest Rate coded in the Plan Specifications - Projection Assumptions. User may check these rates if they like using our Table Maintenance - Functions - Calc Annuity Rates option. You must remember to alter their 'Benefit Date" on the setup screen to reflect a Retirement Age of 67 if you plan uses other than that (e.g. 65). Example: Using the following data: 12/31/2021 plan year end Interest rate of 1.43 (10 year interest rate as of 12/1/2021) RP21C U Mortality table Balance of 135,000 (125,000 Funds, 10,000 Loan) Employee DOB 10/7/1964, Age 67 on 10/7/2031 The system generated APRS are: Single Life = 201.578 J&S 100% = 245.353 The Employee Statement will reflect monthly payments Single Life $135,000/201.578 = 669.72 J&S 100% $135,000/245.353 =550.23 Below is more detail on the APR (Annuity Purchase Rate) which is the present value factor calculated based on the interest, mortality and age assumptions you are assuming. The math used to calculate this is "actuarial" but, in general, an APR is the amount you would need to pay a person $1 from retirement age for the rest of their lives. The calculation of the APR requires Commutation Functions. The Table Maintenance > Commutation Function Reports are used to generate the factors. To calculate the APR at retirement age 67, using RP21C U mortality and a single interest rate of 1.43%, input the following into the Calculate Commutation Functions screen and click Print to generate a report: • Primary Mortality: RP21C U • Interest Rate 1: 1.43 • Prim. Starting Age:67 • Prim. Ending Age: 67 Using the Commutation Functions report output you generated using the output above, you will need the following values: x Dx @ 1.43% Nx12 @ 1.43% 67 360,941.96 6,063,162.41 If you're not familiar with commutation functions, this VERY rough outline will help you understand the use of Nx and Dx: • Nx represents the value of a series of payment of $1 reflecting interest and mortality starting at age x and ending at the last age of the given mortality table. This assumes a single payment at the integer age. The value N12x assumes monthly payments throughout the year. • Dx represents the value of paying $1 reflecting interest and mortality at age x. • For any given interest rate, the APR as of age x of a series of payments of $1 starting at age x and ending at the last age of the given mortality table that you see on the Commutation Functions output is calculated as ax = Nx / Dx. For a monthly annuity, the 12ax = N12x / Dx. With this as the foundation for Commutations Function reporting and use, we can now move to illustrate the calculation of an APR using a single interest rate without deferring to an age before retirement. 1. Calculate the value of monthly payments using interest and mortality (you will use the N12x and Dx values) at retirement age of 67 = Nx12_67/ Dx_67 = 6,063,162.41 / 360,941.96 = 16.7982 2. Multiply the monthly factor by 12 = 16.7982 x 12 = 201.5780