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{"sheet":"Describe","index":0,"n_rows":45,"n_cols":9,"rows_kept":45,"cut":false,"hidden":false,"merged":[]}
["Disclaimer"]
["This software is made available free of charge with the understanding that neither the author nor the Society of Actuaries accepts"]
["any liability for its use. It may be used for any personal, research or commercial use provided that the user does not represent it "]
["as his or her own work and does not distribute it to others for a fee."]
[]
["What"]
["This workbook calculates a 1-dimensional improvement scale and an associated base mortality table that approximate MP-2016 and RP-2014."]
["NOTE: the scale and mortality table go together. Neither can be used by itself."]
["NOTE: the calculated scale is intended as an approximation. It is not suitable as a mortality assumption on its own. Some of the numbers may not make"]
["sense on their own, but the annuity values may be close enough to permit the use of the approximation."]
["The approximation is tuned for single life annuities. It is not necessarily good enough for all types of annuities. See the worksheet \"Comparisons\" to see how"]
["good the approximation is in a variety of cases. This workbook is a tool for an actuary; the actuary remains responsible for exercising proper judgment on"]
["whether the approximation calculated here is appropriate for use in a particular case."]
["If the valuation software can handle a 2-dimensional scale, then using an approximation is extra work with possible loss of accuracy, and therefore, may not be appropriate."]
[]
["How"]
["On the worksheet \"Approximation\", select values for the fields highlighted in yellow. Some of the values must be selected from a drop-down list. The values for"]
["rating, year of calculation, and interest rate are to be keyed in, but there are validation checks to protect against clearly inappropriate values."]
["The field for \"Deferred to age\" is required only if the Annuity type selected is \"Deferred to x\" rather than \"Life\". In this case, enter the age to which annuities"]
["are to be deferred. The calculation is identical to \"Life\" for ages higher than or equal to the \"deferred to\" age."]
["If you select \"Employee\" status (cell B4) for the rates, then you must also specify how to interpolate to the Healthy Annuitant Rates (cells B17,B18). The Employee "]
["rates are used up to and including \"Highest EE age\" (cell B17), and the Healthy Annuitant rates are used for ages beginning with \"Lowest HA age\" (cell B18)."]
["The rates for intervening ages are obtained by multiplying the HA rates by a ratio which is linearly interpolated between the ratio of EE to HA at the \"Highest EE age\" "]
["to 100% at the \"Lowest HA age\"."]
["Interest rates may be specified as a single rate (using cell M5), as 3 PPA segment rates (using cells Q5:Q7),  or a vector of interest rates (using cells M5:M121). The rates used are highlighted in green."]
["There is an option for \"Dataset\": \"manual base table\". Use this option if you wish to provide your own table. It must be entered under the appropriate"]
["headings, starting at cell H4. If you do not provide rates to age 120, the remaining ages will be filled with 1.0. If you use \"manual base table\", you must provide the"]
["base year of the mortality table in cell B11 (pale yellow); otherwise, the base year is calculated by the program."]
["The selection \"Adj to RP-2014\" has changed in this version. Because there is no published mortality table for 2016 to go with MP-2016, you must specify how to"]
["calculate a base table to apply to one year before the calculation year. Each of the selections are described below."]
[null,"\"none\"  The base table is not projected. If you use a manual table, it is your responsibility to ensure that the base year is one prior to \"Year of Calc\"."]
[null,"\"RP-2014 to 2016\"  The published table is projected by two years on MP-2016."]
[null,"\"RP-2014@2006 to 2015/6\"  The published table is projected back to 2006 on MP-2014 and then forward to 2015 or 2016 on MP-2016."]
["NOTE: Year of calculation must be 1 to 4 years after the base year of the table. The approximation is better with a smaller gap."]
[]
["Comments"]
["If you change any of the input parameters, the most recently calculated rates are cleared. The warning message disappears when you click on \"Calculate\"."]
["The interest rates specified are assumed to be spot rates. However, the calculation is done using forward rates which are calculated from the spot rates."]
["\"Joint\" in the Comparison worksheet refers to joint and survivor annuities. The female is assumed to be 3 years younger than the male."]
["The formula for the equivalence in improvement rates is shown below, assuming a calculation year of yc, a base year of yb, life annuities and a flat interest rate."]
[]
[]
["Author"]
["This software was written by RCW (Bob) Howard, FSA, FCIA, September 2014. ",null,null,null,null,null,null,null,"bob@howardfamily.ca"]
["Modified September 2016 to reflect MP-2016."]

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["Create an approximate improvement scale and base mortality table from RP-2014 and MP-2016"]
[null,null,null,"Rates to approximate\r\nMP-2016",null,null,null,"Base q @ 2016 to use with approximate 1D scale"]
["Dataset","Total Dataset",null,"Age","Male","Female",null,"Age","Male","Female",null,"Interest Rates"]
["Status","Healthy Annuitant",null,50,1.16397691256791E-2,1.2594142064592528E-2,null,50,4.0921512420360262E-3,2.7374695117373111E-3,null,"Year","Spot","Forward",null,null,"PPA Segment Rates"]
["Rating",1,null,51,1.3907708936477969E-2,1.4897317954899125E-2,null,51,4.4333720199018463E-3,2.8899764775374109E-3,null,1,0.06,0.06,null,"Years 1-5",0.06]
["Year of calc",2017,null,52,1.5173972780423761E-2,1.6823674420568868E-2,null,52,4.7897219580715703E-3,3.0708456140586139E-3,null,2,0.06,0.06,null,"Years 5-20",5.5E-2]
["Annuity","Life",null,53,1.6504458141422651E-2,1.826172905396628E-2,null,53,5.1293805875539779E-3,3.2799884022125395E-3,null,3,0.06,0.06,null,"Years 21+",0.05]
["Deferred to",null,null,54,1.7441462841217947E-2,1.8972668791500169E-2,null,54,5.4739332867987881E-3,3.519381203071042E-3,null,4,0.06,0.06]
["Interest","Flat rate in cell J5",null,55,1.7776749285628557E-2,1.9229504533322617E-2,null,55,5.8308620069380517E-3,3.788998810982352E-3,null,5,0.06,0.06]
["Adj to RP-2014","RP-2014@2006 to 2016",null,56,1.7781464732229302E-2,1.8262271881345327E-2,null,56,6.2086264278507081E-3,4.0875712376987009E-3,null,6,0.06,0.06]
["Base yr to qx",2016,null,57,1.764030609595213E-2,1.689861415877647E-2,null,57,6.6126509653445485E-3,4.4183844479555607E-3,null,7,0.06,0.06]
[null,null,null,58,1.6850737500945012E-2,1.5036147503732944E-2,null,58,7.0499939174073819E-3,4.7801286500500813E-3,null,8,0.06,0.06]
[null,null,null,59,1.6044726362269279E-2,1.26205351084967E-2,null,59,7.5246741219234933E-3,5.1769623791432301E-3,null,9,0.06,0.06]
[null,null,null,60,1.4719378564462593E-2,9.6044349928601225E-3,null,60,8.0472729591691636E-3,5.6058444156780306E-3,null,10,0.06,0.06]
[null,null,null,61,1.3521968629285674E-2,7.3217609888610591E-3,null,61,8.6192383785633573E-3,6.0782189034384098E-3,null,11,0.06,0.06]
["Interpolation if using Employee rates",null,null,62,1.1762708769245234E-2,4.6058175724570383E-3,null,62,9.2461857884659892E-3,6.5905411570114075E-3,null,12,0.06,0.06]
["Highest EE age",70,null,63,1.0166178965955397E-2,3.1924767324656989E-3,null,63,9.9343059158235776E-3,7.1465622914135742E-3,null,13,0.06,0.06]
["Lowest HA age",80,null,64,8.3139085789566414E-3,2.0903362423420058E-3,null,64,1.0695623139468698E-2,7.7634400568456462E-3,null,14,0.06,0.06]
[null,null,null,65,6.9309561520036755E-3,1.7717638787014822E-3,null,65,1.152781427742176E-2,8.4434426672782021E-3,null,15,0.06,0.06]
[null,null,null,66,5.3308915100680476E-3,1.8320279043363419E-3,null,66,1.2453260916182035E-2,9.2007881306529742E-3,null,16,0.06,0.06]
[null,null,null,67,4.2464894923799346E-3,2.9688826100080501E-3,null,67,1.3472317789629693E-2,1.0050175985638211E-2,null,17,0.06,0.06]
[null,null,null,68,3.6330618500918233E-3,4.0130007298826431E-3,null,68,1.4614132709119798E-2,1.0999610941293265E-2,null,18,0.06,0.06]
[null,null,null,69,3.3160719691993634E-3,5.3377709712766341E-3,null,69,1.5906358839383752E-2,1.2064538089614258E-2,null,19,0.06,0.06]
[null,null,null,70,4.186880800795878E-3,7.3354101870126698E-3,null,70,1.7359044227160614E-2,1.3256405923155409E-2,null,20,0.06,0.06]
[null,null,null,71,4.8498369440189704E-3,8.5333740751675213E-3,null,71,1.8987178675456795E-2,1.4597112693545257E-2,null,21,0.06,0.06]
[null,null,null,72,5.7406889479553191E-3,9.5338421711658183E-3,null,72,2.0831027469124502E-2,1.6084863999160672E-2,null,22,0.06,0.06]
[null,null,null,73,6.9409258848928124E-3,1.0395206966357651E-2,null,73,2.2907037933036219E-2,1.7753871607161242E-2,null,23,0.06,0.06]
[null,null,null,74,7.8329584471076297E-3,1.122743619120492E-2,null,74,2.5240038293039505E-2,1.9618088817199539E-2,null,24,0.06,0.06]
[null,null,null,75,8.4886875255087979E-3,1.158217882329704E-2,null,75,2.7866713565012673E-2,2.1704230048351671E-2,null,25,0.06,0.06]
["none",null,null,76,9.1859903633333406E-3,1.1689864597849597E-2,null,76,3.0829207970237724E-2,2.4048686563577927E-2,null,26,0.06,0.06]
["RP-2014 to 2016",null,null,77,9.8230442253675054E-3,1.2015395958665298E-2,null,77,3.4158371397519573E-2,2.6687588938505896E-2,null,27,0.06,0.06]
["RP-2014@2006 to 2015",null,null,78,1.0367173090313986E-2,1.208923554252983E-2,null,78,3.793856643493948E-2,2.9683460917919069E-2,null,28,0.06,0.06]
["RP-2014@2006 to 2016",null,null,79,1.0403928254777539E-2,1.2125344831386609E-2,null,79,4.2177737114229591E-2,3.3080093902583582E-2,null,29,0.06,0.06]
[null,null,null,80,1.1361280462052648E-2,1.2425636179252963E-2,null,80,4.6989165214542224E-2,3.6930774057876377E-2,null,30,0.06,0.06]
["Total Dataset",null,null,81,1.1228524907879955E-2,1.2077640003204104E-2,null,81,5.2419201592969401E-2,4.134375645650059E-2,null,31,0.06,0.06]
["Blue Collar",null,null,82,1.1187313032756774E-2,1.168404029956871E-2,null,82,5.8563515123488605E-2,4.6316933914629363E-2,null,32,0.06,0.06]
["White Collar",null,null,83,1.1221067367287785E-2,1.1079843812438095E-2,null,83,6.5485136747124528E-2,5.1998526101858802E-2,null,33,0.06,0.06]
["Top Quartile",null,null,84,1.077616045166252E-2,1.0494210053966002E-2,null,84,7.3336161222591414E-2,5.8424371377702677E-2,null,34,0.06,0.06]
["Bottom Quartile",null,null,85,1.0819245109197628E-2,9.7777434728478774E-3,null,85,8.2127849231973318E-2,6.5676022676944751E-2,null,35,0.06,0.06]
["manual base table",null,null,86,1.0323087688288823E-2,9.2149521816115021E-3,null,86,9.1983407622273514E-2,7.3814669355157125E-2,null,36,0.06,0.06]
[null,null,null,87,9.9907536339128855E-3,8.766520010160983E-3,null,87,0.10301698347797651,8.2923013266499201E-2,null,37,0.06,0.06]
[null,null,null,88,9.7976285982092071E-3,8.1109188235277685E-3,null,88,0.11527730728094146,9.3016726685417911E-2,null,38,0.06,0.06]
[null,null,null,89,9.4647118232672467E-3,7.8844668804131102E-3,null,89,0.1288571318960107,0.10415483912639374,null,39,0.06,0.06]
[null,null,null,90,9.1364432160594422E-3,7.4668547137040076E-3,null,90,0.14385509459191542,0.11650662547885267,null,40,0.06,0.06]
[null,null,null,91,8.775377182295041E-3,7.3547598470078412E-3,null,91,0.15966026226702218,0.12985641466054898,null,41,0.06,0.06]
[null,null,null,92,8.6048470833051116E-3,7.3585098255691817E-3,null,92,0.17578155393700162,0.14399477799807125,null,42,0.06,0.06]
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[null,null,null,96,8.2685719071630137E-3,7.2790061958976082E-3,null,96,0.24209258650881105,0.20705884469295244,null,46,0.06,0.06]
[null,null,null,97,7.9352295694938846E-3,6.9409817705596843E-3,null,97,0.26067449324019376,0.22502943991094293,null,47,0.06,0.06]
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[null,null,null,101,6.2278466106601149E-3,5.4037582702655129E-3,null,101,0.34010749229395038,0.30312297792644188,null,51,0.06,0.06]
[null,null,null,102,5.7847722600747886E-3,5.0801168535801189E-3,null,102,0.36017261045283677,0.32341335582209163,null,52,0.06,0.06]
[null,null,null,103,5.4019254263447669E-3,4.7118747586385457E-3,null,103,0.37998179077477645,0.34370567692595588,null,53,0.06,0.06]
[null,null,null,104,5.0241405317069665E-3,4.3016929574516416E-3,null,104,0.39919312805138946,0.36357407446859746,null,54,0.06,0.06]
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[null,null,null,108,3.2228936845205558E-3,2.8180185678811087E-3,null,108,0.46849073196663732,0.43783242933572442,null,58,0.06,0.06]
[null,null,null,109,2.6647039624582147E-3,2.4733154108138589E-3,null,109,0.48352416943176285,0.45433053902589737,null,59,0.06,0.06]
[null,null,null,110,2.3413892111245893E-3,1.9625655344076565E-3,null,110,0.49736556933418508,0.46980573892217087,null,60,0.06,0.06]
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[null,null,null,118,0,0,null,118,0.5,0.5,null,68,0.06,0.06]
[null,null,null,119,0,0,null,119,0.5,0.5,null,69,0.06,0.06]
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[null,null,null,null,null,null,null,null,null,null,null,106,0.06,0.06]
[null,null,null,null,null,null,null,null,null,null,null,107,0.06,0.06]
[null,null,null,null,null,null,null,null,null,null,null,108,0.06,0.06]
[null,null,null,null,null,null,null,null,null,null,null,109,0.06,0.06]
[null,null,null,null,null,null,null,null,null,null,null,110,0.06,0.06]
[null,null,null,null,null,null,null,null,null,null,null,111,0.06,0.06]
[null,null,null,null,null,null,null,null,null,null,null,112,0.06,0.06]
[null,null,null,null,null,null,null,null,null,null,null,113,0.06,0.06]
[null,null,null,null,null,null,null,null,null,null,null,114,0.06,0.06]
[null,null,null,null,null,null,null,null,null,null,null,115,0.06,0.06]
[null,null,null,null,null,null,null,null,null,null,null,116,0.06,0.06]
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{"sheet":"Comparisons","index":2,"n_rows":55,"n_cols":30,"rows_kept":55,"cut":false,"hidden":false,"merged":[[2,1,2,9],[2,11,2,19],[3,12,3,13],[3,14,3,15],[3,16,3,17],[3,18,3,19],[20,1,20,9],[20,11,20,19],[20,21,20,29],[3,2,3,3],[3,4,3,5],[3,6,3,7],[3,8,3,9],[2,21,2,29],[3,22,3,23],[3,24,3,25],[3,26,3,27],[3,28,3,29],[21,28,21,29],[21,2,21,3],[21,4,21,5],[21,6,21,7],[21,8,21,9],[21,12,21,13],[21,14,21,15],[21,16,21,17],[21,18,21,19],[21,22,21,23],[21,24,21,25],[21,26,21,27],[38,1,38,9],[38,11,38,19],[38,21,38,29],[39,2,39,3],[39,4,39,5],[39,6,39,7],[39,8,39,9],[39,12,39,13],[39,14,39,15],[39,16,39,17],[39,18,39,19],[39,22,39,23],[39,24,39,25],[39,26,39,27],[39,28,39,29]]}
["Comparing the exact and approximate calculation of present values of monthly annuities-due"]
["The numbers shown are (approximate - exact)/exact",null,null,null,null,null,null,null,null,null,null,"Calculations for later years use the same spot rate yield curve as the earlier year."]
[null,"As of January 1, 2017 at 6.0% interest with a mortality rating of 100%",null,null,null,null,null,null,null,null,null,"As of January 1, 2018 at 6.0% interest with a mortality rating of 100%",null,null,null,null,null,null,null,null,null,"As of January 1, 2019 at 6.0% interest with a mortality rating of 100%"]
[null,null,"Single Life",null,"10-year Certain",null,"Joint Unreduced",null,"Jt Reducing to 60%",null,null,null,"Single Life",null,"10-year Certain",null,"Joint Unreduced",null,"Jt Reducing to 60%",null,null,null,"Single Life",null,"10-year Certain",null,"Joint Unreduced",null,"Jt Reducing to 60%"]
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[]
[null,"As of January 1, 2017 at 4.0% interest with a mortality rating of 100%",null,null,null,null,null,null,null,null,null,"As of January 1, 2018 at 4.0% interest with a mortality rating of 100%",null,null,null,null,null,null,null,null,null,"As of January 1, 2019 at 4.0% interest with a mortality rating of 100%"]
[null,null,"Single Life",null,"10-year Certain",null,"Joint Unreduced",null,"Jt Reducing to 60%",null,null,null,"Single Life",null,"10-year Certain",null,"Joint Unreduced",null,"Jt Reducing to 60%",null,null,null,"Single Life",null,"10-year Certain",null,"Joint Unreduced",null,"Jt Reducing to 60%"]
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[]
[null,"As of January 1, 2017 at 8.0% interest with a mortality rating of 100%",null,null,null,null,null,null,null,null,null,"As of January 1, 2018 at 8.0% interest with a mortality rating of 100%",null,null,null,null,null,null,null,null,null,"As of January 1, 2019 at 8.0% interest with a mortality rating of 100%"]
[null,null,"Single Life",null,"10-year Certain",null,"Joint Unreduced",null,"Jt Reducing to 60%",null,null,null,"Single Life",null,"10-year Certain",null,"Joint Unreduced",null,"Jt Reducing to 60%",null,null,null,"Single Life",null,"10-year Certain",null,"Joint Unreduced",null,"Jt Reducing to 60%"]
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{"sheet":"Sample Qx Calc","index":3,"n_rows":31,"n_cols":23,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["This worksheet contains sample calculations of mortality rates that may be useful in testing software for a 2-dimensional improvement scale. The approximate improvement scale is not used."]
["Table:","RP-2014 Total Dataset Healthy Annuitant"]
["Scale:","MP-2016"]
["Sex:","Male"]
["Age\\Year",2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035]
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["RP-2014 Rates: Total Dataset"]
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{"sheet":"Blue Collar","index":5,"n_rows":107,"n_cols":8,"rows_kept":107,"cut":false,"hidden":false,"merged":[[2,3,2,4],[2,6,2,7]]}
["RP-2014 Rates: Blue Collar"]
[]
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{"sheet":"White Collar","index":6,"n_rows":107,"n_cols":8,"rows_kept":107,"cut":false,"hidden":false,"merged":[[2,3,2,4],[2,6,2,7]]}
["RP-2014 Rates: White Collar"]
[]
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{"sheet":"Bottom Quartile","index":7,"n_rows":107,"n_cols":8,"rows_kept":107,"cut":false,"hidden":false,"merged":[[2,3,2,4],[2,6,2,7]]}
["RP-2014 Rates: Bottom Quartile"]
[]
[null,null,null,"Bottom Quartile; Males",null,null,"Bottom Quartile; Females"]
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[]
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{"sheet":"Factors","index":11,"n_rows":123,"n_cols":3,"rows_kept":123,"cut":false,"hidden":false,"merged":[]}
["Factors to adjust RP-2014 to 2006, based on MP-2014"]
["Age","Male","Female"]
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