Excel Functions in EAC ToolsExcel Functions in EAC Tools\Actuarial equivalence functionsActuarial equivalence functions\AESLtoLI

AESLtoLI

AESLtoLI calculates an actuarial equivalent factor to convert a straight life annuity to a life annuity with a level income option based the leveling age and fraction, and assumptions for interest, mortality, and the values for the following parameters.

where 𝐴𝐸𝐹𝑎𝑐𝑡𝑜𝑟 is defined as:

Syntax

AESLtoLI (CurrentAge, CommencementAge, LevelAge, LevelFraction, InterestRate, MortalityTable, [YearsCertain], [AgeSetback], [Frequency], [COLA], [CalculationMethod], [NoPreRetMort], [AnnTiming])

Parameter Name

Description

CurrentAge

Age at valuation.

CommencementAge

Age at benefit commencement.

LevelAge

Age at which amount of annuity changes for the leveling option.

LevelFraction

Fraction of the original payment amount to be paid starting at LevelAge.

Where

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

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

 

 

AESLtoLI calculates an actuarial equivalent factor to convert a straight life annuity to a life annuity with a level income option based the leveling age and fraction, and assumptions for interest, mortality, and the values for the following parameters.

where AEFactor is defined as:

Syntax

AESLtoLI (CurrentAge, CommencementAge, LevelAge, LevelFraction, InterestRate, MortalityTable, [YearsCertain], [AgeSetback], [Frequency], [COLA], [CalculationMethod], [NoPreRetMort], [AnnTiming])

Parameter Name

Description

CurrentAge

Age at valuation.

CommencementAge

Age at benefit commencement.

LevelAge

 

LevelFraction

 

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

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