An interest rate assumption is used in the actuarial present value calculation in order to determine the discounted value of financial events occurring in the future. While it is easiest to use a single fixed rate, it is common for interest rates to vary over time. EAC Tools allows a variety ways to define the interest rate parameter that is to be used in the functions.

Basic interest functions

1.	annual effective interest rate
2.	nominal interest rate convertible 𝑚 times per year
3.	discount rate = the present value of 1 due in 1 year
4.	the present value of 1 due in 𝑛 years

 

Types of interest rates

To get detailed information about a specific type of interest rate, click its name in the first column.

Type of Interest Rate	Description
Single rate	This is the simplest use of the interest rate assumption – one rate that applies for all time.
PPA segment rates	Three “spot rates” that are used to discount future payments, as required by the Pension Protection Act of 2006
Deferred and immediate rates	One or more rates that apply during the deferred period (prior to commencement), and a different rate that applies during payment (after commencement).
Select and ultimate rates	One rate that applies for a given number of years, and a different rate that applies thereafter.
Spot rates	Specific interest rates that are used to discount each future payment.
Forward rates	Various rates that apply over time, compounded to discount future payments.

Single rate

This is the simplest use of the interest rate assumption – one single rate that applies for all time.

The present value at age 𝑥 of a life annuity of 1 per year, payable at the beginning of the year is calculated by this formula:

 

PPA segment rates

Also called minimum present value segment rates or applicable interest rates, the PPA segment rates are published monthly by the IRS and mandated under Section 417(e)(3)(D) of the Code for calculation of the minimum lump sum equivalent of an annuity. This was the result of the Pension Protection Act of 2006 (PPA) and was effective in the plan year beginning in 2008. Note that is an example of the use of “spot rates”.

·        The 1^st segment rate 𝑖1 is used to discount amounts paid during the first 5 years,

·        The 2^nd segment rate 𝑖2 is used to discount amounts paid during the next 15 years,

·        The 3^rd segment rate 𝑖3 is used to discount amounts paid thereafter.

The present value at age 𝑥 of a life annuity of 1 per year, payable at the beginning of the year is calculated by this formula:

It is easy to use PPA segment rates for the EAC Tools interest parameter.

 

Deferred and immediate rates

One or more rates that apply during the deferred period (prior to commencement), and a different rate that applies during payment (after commencement). For example, assuming the following deferred and immediate rates:

·       Deferred rates:

-   𝑖1 for first 7 years of deferral,

-   𝑖2 for next 8 years of deferral,

-   𝑖3 thereafter during deferral,

·       Immediate rate:

-   𝑖4 during payment,

the present value at age 45 of a life annuity of 1 per year, commencing at age 65, payable at the beginning of the year is calculated by this formula,

Deferred and immediate rates can be used for the EAC Tools interest parameter as follows:

·        Deferred and immediate 2 rates

·        Deferred and immediate PBGC 4 rates

 

Select and ultimate rates

One rate that applies for a certain number of years, and another rate that applies thereafter. For example, assuming the following select and ultimate rates:

·       Select rate:        𝑖1 for the first 25 years,

·       Ultimate rate:    𝑖2 thereafter.

The present value at age 45 of a life annuity of 1 per year, commencing at age 65, payable at the beginning of the year is calculated by this formula,

Note that is an example of the use of “forward rates”.

Select and ultimate rates can be used for the EAC Tools interest parameter as follows:

·        Select and ultimate 20 years for ERISA 4044 annuities

·        Select and ultimate 25 years for ERISA 4044 annuities

 

Spot rates

Spot rates are used to discount the payment in each year with a specific interest rate that applies for that year. This is commonly used to apply a yield curve of spot rates for maturities of varying duration in order to calculate the discounted value of a future stream of payments.

·        Rate 𝑖1 is used to discount the payment in year 1,

·        Rate 𝑖2 is used to discount the payment in year 2,

·        Rate 𝑖3 is used to discount the payment in year 3, …

The present value at age 𝑥 of a life annuity of 1 per year, payable at the beginning of the year is calculated by this formula:

Spot rates are available from the ERISA 4044 interest assumption (for valuation dates on or after July 31, 2024), The Treasury High Quality Market (HQM) Corporate Bond Yield Curve published on the IRS web site for Monthly Yield Curve Tables, and also from the FTSE Pension Discount Curve published on the Yield Book web site for FTSE Pension Liability Index.

Spot rates can be used for the EAC Tools interest parameter as follows:

·        spot rates from an IRS yield curve

·        spot rates from an ERISA 4044 yield curve

·        spot rates from an FTSE yield curve

·        spot rates from a FTSE Above Median Double-A Curve

·        spot rates from your own array of rates

 

Forward rates

Forward rates are a series of interest rates compounded over time to discount a future stream of payments.

The present value at age 𝑥 of a life annuity of 1 per year, payable at the beginning of the year is calculated by this formula:

ERISA 4044 select and ultimate rates are a special case of forward rates.

Forward rates from your own array of rates can be used for the EAC Tools interest parameter.