Actuarial Tools

Browse all available actuarial tools.

Available tools

Accumulation Factor Calculator Actualconstantforceaccumulatione^(δt),not selectinterestforecast Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Aggregate Excess Loss Layer Calculator Calculate the aggregate loss falling within a layer above an attachment point, capped by the layer limit.
Annuity Due Present Value Calculator Actual Annuity Due Present Value Calculatorexplicitcashflowtimingperiods;unitpaymentbaseincludingdeclaredincreasing/decreasing/geometricweights,no embeddedmortality/contractpolicy. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Annuity Immediate Present Value Calculator Actual Annuity Immediate Present Value Calculatorexplicitcashflowtimingperiods;unitpaymentbaseincludingdeclaredincreasing/decreasing/geometricweights,no embeddedmortality/contractpolicy. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Apportionable Premium Factor Calculator Calculate the apportionable premium factor that adjusts an annual premium for installment payment frequency assuming claims occur uniformly over the year.
Balducci Fractional Survival Calculator Interpolate survival within the year under the Balducci hypothesis of hyperbolic mortality density.
Bornhuetter-Ferguson Reserve Calculator Estimate the IBNR reserve with the Bornhuetter-Ferguson method from earned premium, the expected loss ratio, and the portion of losses not yet reported.
Buhlmann-Straub Credibility Factor Calculator Weight experience against the prior mean using the Buhlmann-Straub credibility factor from total exposure and the variance components.
Central Death Rate Mx Calculator Actualcentraldeathratemx=d/personyearsexposure,not populationfractionqx. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Chain Ladder Development Factor Calculator Calculate the volume-weighted chain ladder age-to-age development factor from paired cumulative losses.
Commutation Function Cx Calculator CommutationC_x=v^(x+1)d_xendyearmortalitydiscount,notv^xD_x. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Commutation Function Dx Calculator CommutationD_x=v^x l_xdefinedabsoluteageexponent,not deferredNPVpayment. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Commutation Function Mx Calculator CommutationM_x=Σk≥xC_k,actualcompleteCxsequence. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Commutation Function Nx Calculator CommutationN_x=Σk≥xD_k,independentlycompleteactualtailprovided,no mortalitytableinvented. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Commutation Function Rx Calculator CommutationR_x=Σk≥x(k−x+1)C_k=ΣM_k,actualcompleteCxsequence. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Complete Expectation of Life Calculator Closedannualtable completeUDDwithinyearlifeexpectationtrapezoid integral of survival,lastqx1andcompleteobservedtail. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Compound Poisson Total Variance Calculator Calculate the variance of aggregate claims for a compound Poisson model as the claim frequency times the second moment of severity.
Constant Force Fractional Survival Calculator Interpolate survival within the year under a constant force of mortality.
Contingent Insurance Probability Calculator Calculate the probability that the first life dies before the second life under constant forces of mortality derived from annual death probabilities.
Continuous Whole Life EPV Calculator Calculate the expected present value of a continuously paying whole life insurance under a constant force of mortality derived from the annual death probability.
Continuous Whole Life Present Value Second Moment Calculator Calculate the second moment of a continuous whole-life insurance present value under constant forces of mortality and interest.
CRVM Modified Reserve Calculator Calculate a Commissioners Reserve Valuation Method modified premium and prospective reserve for a level-premium policy from precomputed actuarial present values.
Curtate Expectation of Life Calculator Closedannualtable curtatelifeexpectationΣk≥1p_x(k),lastqx1andcompleteobservedtail. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
De Moivre Uniform Death Survival Calculator DeMoivrelinearuniform-lifetimeconditional survival(ω−x−t)/(ω−x),0≤x<ω,0≤t≤ω−x. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Decreasing Annuity Immediate Calculator Actual Decreasing Annuity Immediate Calculatorexplicitcashflowtimingperiods;unitpaymentbaseincludingdeclaredincreasing/decreasing/geometricweights,no embeddedmortality/contractpolicy. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Decreasing Term Insurance EPV Calculator Calculate the expected present value of an n-year decreasing term insurance whose benefit steps down by one each year of the term.
Deferred Annuity Present Value Calculator Actual Deferred Annuity Present Value Calculatorexplicitcashflowtimingperiods;unitpaymentbaseincludingdeclaredincreasing/decreasing/geometricweights,no embeddedmortality/contractpolicy. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Deferred Mortality Probability Calculator Actualdeferreddeathsurvivefirstmthen dieinnconditionalannualtable,nopayoutdiscountor deferredtermEPV. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Deferred Term Insurance EPV Calculator Calculate the expected present value of an n-year term insurance whose coverage starts after the deferment period.
Deferred Whole Life EPV Calculator Calculate the expected present value of a whole life insurance whose death benefit applies only after the deferment period.
Dependent to Independent Decrement Converter Recover the single-cause independent annual decrement rate from its dependent multiple-decrement table rate assuming constant forces within the year.
Discount Factor V Power N Calculator Discountv^n Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Discount Rate to Effective Interest Converter Discountd→effectivei=d/(1−d) Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Effective Interest to Discount Rate Converter Effectivei→discountd=i/(1+i) Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Endowment Insurance EPV Calculator Calculate the expected present value of an endowment insurance paying on death during the term or on survival to maturity.
Entry Age Normal Liability Calculator Allocate a projected lump-sum retirement benefit to level annual normal costs from entry age to retirement and calculate the accrued liability for completed service.
Expected Loss Ratio Calculator Calculate an expected loss ratio by dividing selected expected losses by earned premium for the same exposure period.
Expected Loss Ratio IBNR Calculator Estimate unreported losses by subtracting reported incurred losses from expected ultimate losses implied by an expected loss ratio.
Experience Modification Factor Calculator Calculate a workers' compensation experience modification factor using primary losses, weighted excess losses, expected losses, and a ballast value.
Fackler Reserve Step Calculator Advance a policy reserve one year with the Fackler step: accumulate reserve plus premium at interest, pay expected claims, and share the fund among survivors.
Final Average Salary Calculator Average the most recent years in a salary history to obtain the final average salary used as an input to defined-benefit pension formulas.
Force of Interest Delta Calculator Forceinterestδ=ln(1+i) Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Force of Mortality From lx Calculator IntervalAVERAGEforce−ln(lend/lstart)/Δ,not pointderivativewithoutagegrid. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Frequency Severity Expected Loss Calculator Multiply expected claim frequency by average claim severity to obtain the expected loss.
Full Preliminary Term Reserve Calculator Calculate the full preliminary term valuation: the first year funds only a one-year term cost leaving zero terminal reserve, and later years use the renewal valuation premium.
Geometric Increasing Annuity Calculator Actual Geometric Increasing Annuity Calculatorexplicitcashflowtimingperiods;unitpaymentbaseincludingdeclaredincreasing/decreasing/geometricweights,no embeddedmortality/contractpolicy. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Gompertz Law Force of Mortality Calculator Conditional Gompertz law μ(x)=B c^x for independently calibrated B>0, c>1, in inverse years, with integrated next-year hazard and exp(−hazard) survival. These are explicit actuarial model assumptions, not observed individual death probability, diagnosis, life expectancy, clinical advice or a published mortality table.
Gross Premium Expense Loading Calculator Load a net premium with a fixed expense and a variable expense ratio to obtain the gross premium.
Hazard Consistency Checker Check whether an annual death probability matches a constant force of mortality within a tolerance.
Increasing Annuity Immediate Calculator Actual Increasing Annuity Immediate Calculatorexplicitcashflowtimingperiods;unitpaymentbaseincludingdeclaredincreasing/decreasing/geometricweights,no embeddedmortality/contractpolicy. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Increasing Whole Life EPV Calculator Calculate the expected present value of a whole life insurance whose death benefit steps up by one unit each year.
Independent to Dependent Decrement Converter Convert an independent annual decrement rate into its dependent multiple-decrement table rate assuming constant forces within the year.
Joint Life Annuity EPV Calculator Calculate the expected present value of an annuity-due that continues while both independent lives survive.
Joint Life Expectation Calculator Calculate the complete expected lifetime of the joint status of two independent lives under constant forces of mortality derived from annual death probabilities.
Joint Life Survival Probability Calculator Calculate the probability that two independent lives both survive the given number of years.
Last Survivor Annuity EPV Calculator Calculate the expected present value of an annuity-due that continues while at least one of two independent lives survives.
Last Survivor Expectation Identity Calculator Calculate the last survivor life expectancy using the identity that combines both single-life expectancies minus the joint life expectancy.
Last Survivor Probability Calculator Calculate the probability that at least one of two independent lives survives the given number of years.
Life Table Dx Deaths Calculator Actuald_x=l_xq_xexpectedcohortdeaths,mayscalefractional,not individualeventcounts. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Life Table Lx Scaling Calculator Lowercasel_xradixrescalingNOTuppercasepersonyearsL_x,actualtablevaluesnonincreasing. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Limited-Fluctuation Credibility Factor Calculator Assign partial credibility to experience with the square root rule relative to the full credibility claim count.
Makeham Law Force of Mortality Calculator DeclaredMakehamμ(x)=A+B c^x,c>1,compatibleinverseyears,not GompertzwithoutA. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Monthly Premium Conversion Calculator Convert an annually payable premium into twelve equal monthly installments with the same present value at the given effective interest rate.
Multi-Year Death Probability tQx Calculator Conditionalwholeyeardeath1−Πpxfromactualsequenceqx,not constanthazardassumed. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Multi-Year Survival Probability tPx Calculator ConditionalwholeyearsurvivalΠpxfromactualsequenceqx,not constanthazardassumed. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Mx to Qx Converter Actual n-yearqx=nmx/[1+(n−a)mx],aindependentlyknownwithininterval,noUDDforced. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
N-Year Temporary Life Annuity-Due Calculator Calculate the present value of an n-year temporary life annuity-due paying at the start of each year while the life survives.
Net Level Annual Premium Calculator Calculate the net level annual premium whose expected present value funds a whole life benefit paid at the end of the year of death.
Net Single Premium Calculator Calculate the net single premium that funds a whole life benefit paid at the end of the year of death.
Nominal to Effective Interest P-thly Converter Nominalj convertiblep times→effective(1+j/p)^p−1 Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Normal Retirement Benefit Calculator Calculate the annual pension benefit from final average salary, an accrual rate per service year, and completed years of service.
Perpetuity Due Present Value Calculator Levelinfiniteperpetuity duefirstpaymentnow,actualconstantpositiveinterest/no mortaltail. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Perpetuity Immediate Present Value Calculator Levelinfiniteperpetuity immediatefirstpaymentperiod1,actualconstantpositiveinterest/no mortaltail. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Probability First Cause Calculator Calculate the probability that a given cause of decrement is the first to remove the life, using constant hazards derived from independent annual rates.
Probability of Death qx Calculator Actuallife-tableqx=d_x/l_x,countsnotcentraldeathrate.
Probability of Survival px Calculator Actualintervalpx=1−qx,not fittedsurvival or human individualrisk. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Projected Salary Accrual Present Value Calculator Project a salary-based benefit accrual to its payment date and discount that single future amount to present value.
Proportional Reinsurance Retained Variance Calculator Calculate retained aggregate-loss variance after proportional reinsurance by multiplying total variance by the square of the retained share.
Prospective Net Reserve Calculator Calculate the prospective net reserve as the value of future benefits minus future net premiums on the renewal mortality basis.
Pure Endowment EPV Calculator Calculate the expected present value of a pure endowment paying only if the life survives the full term.
Quarterly Premium Conversion Calculator Convert an annually payable premium into four equal quarterly installments with the same present value at the given effective interest rate.
Qx to Mx Converter Actual inversecentralratemx=qx/[n−(n−a)qx],independenta/no constanthazardassumption. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Retrospective Net Reserve Calculator Calculate the retrospective net reserve as accumulated net premiums minus the accumulated cost of insurance, shared among survivors at the stated duration.
Reversionary Annuity EPV Calculator Calculate the expected present value of an annuity payable while the second life survives after the first life has died, assuming independent lives.
Semiannual Premium Conversion Calculator Convert an annually payable premium into two equal semiannual installments with the same present value at the given effective interest rate.
Stop-Loss Normal Approximation Expected Cost Calculator Estimate the expected aggregate loss above an attachment point under a normal approximation, before expenses or risk loads.
Temporary Complete Expectation Calculator TemporaryUDDwithin-yearcompleteexpectationintegral0…n(actualtable),not assumeopen tailzero or discountannuity. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Term Insurance EPV Calculator Calculate the expected present value of an n-year term life insurance paying at the end of the year of death within the term.
Term Life Annuity EPV Calculator Calculate the expected present value of an n-year temporary life annuity-immediate paying at the end of each survived year.
Total Decrement Rate Calculator Combine independent causes of decrement into the total probability of leaving active status during the year.
UDD Fractional Survival Calculator Interpolate survival within the year under the uniform distribution of deaths assumption.
Unearned Premium Pro Rata Calculator Split a written premium into the unearned portion on a straight-line pro rata temporis basis.
Weibull Hazard Survival Calculator QualifiedWeibullμ=(k/λ)(x/λ)^(k−1),S=e^−(x/λ)^k,positive-agebranch/no zero-age singularity or silentunderflow. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Whole Life Annuity Due EPV Calculator Calculate the expected present value of a whole life annuity-due paying at the start of every survived year.
Whole Life Insurance EPV Calculator Calculate the expected present value of a whole life insurance paying at the end of the year of death.
Withdrawal Probability Service Table Calculator Calculate the probability an active member is still in service after the given years, and the cumulative chance they have withdrawn.
Zillmer Reserve Calculator Calculate the Zillmer reserve, which raises the valuation premium to recover a per-unit first-year expense allowance and values the policy prospectively with that modified premium.