EIRSL

EIRSL calculates the effective interest rate for single life annuity based on the same parameters that are used for the PVSL function. When using spot rates, forward rates, deferred & immediate rates, select & ultimate rates, segment rates, this returns the single interest rate that produces the same present value. (Obviously, this is not useful when using a single interest rate.)

Syntax

EIRSL (CurrentAge, CommencementAge, InterestRate, MortalityTable, [YearsCertain], [AgeSetback], [Frequency], [COLA], [CalculationMethod], [NoPreRetMort], [StopAge], [AnnTiming], [YrsCertOption])

Parameter Name

Description

CurrentAge

Current age of the annuitant (i.e. the age at the valuation date). May be provided as an integer, or as a fractional amount (e.g. years & months).

CommencementAge

Age of annuitant at benefit commencement.

· If CommencementAge > CurrentAge then it will be valued as a deferred annuity.

· If CommencementAge is missing or zero, then CommencementAge is assumed to be = CurrentAge and it will be valued as an immediate annuity

InterestRate

The interest rate(s) to discount future payments to calculate the present value. May be a number, a percentage, a text string, a named range, or reference to a range.

· Rates can be defined using these interest definitions.

· Note: A value that is greater than 25% (i.e. 0.25) will be divided by 100; e.g. if you enter 2.75 it will be treated as .0275 or 2.75%.

MortalityTable

Mortality table definition text string.

YearsCertain

Number of years guaranteed payments. May be an integer, or a factional amount (e.g. years & months).
Optional, default = 0

AgeSetback

Mortality table age set-back. A negative number is a set-forward.
Note that you can also define a setback using the "/sb" option in the table definition (or "/sf").
Optional, default = 0.

Frequency

Number of payments per year:
Optional, default = 12

Frequency	Description
1	annual
2	semi-annual
4	quarterly
6	bi-monthly
12	monthly
99	continuous

COLA

Periodic cost-of-living adjustment applied to the benefit amount.
Optional, default = 0
Rates can be defined using these COLA definitions.

CalculationMethod

Method of calculation
Optional, default = 0

Method	Calculation Approach	How to Handle
Method	Calculation Approach	Fractional Ages	Frequency of Payments
0	discounted cash flow	interpolate on whole ages	Woolhouse
1	discounted cash flow	exact	exact
2	discounted cash flow	exact	Woolhouse
8	commutation functions	interpolate on 𝑙𝑥	Woolhouse
9	commutation functions	interpolate on 𝐷𝑥	Woolhouse

NoPreRetMort

The defines the application of pre-retirement mortality for a deferred annuity.
Optional, default = 0.

NoPreRetMort	Description
0	use pre-retirement mortality
1	no pre-retirement mortality

StopAge

Age when the annuity benefit stops -- no payment at this age.
Optional, default = to end of the mortality table.

AnnTiming

Defines when the payments are made in the period.
Optional, default = 0.

AnnTiming	Description
0	beginning of period
1	end of period
0 to 1	fraction of period, e.g. .5 means paid in middle of the period

YrsCertOption

This is to select the method of calculation for the certain portion of the annuity when using CalculationMethod =0. It does not apply for other methods. This is used only if YearsCertain not a whole number.
Optional, default = 0.

YrsCertOption	Description
0	interpolate on whole numbers
1	exact certain period + deferred annuity