A more thorough explanation:

Actuarial equivalent refers to the amount of pension benefits that are accrued and paid out over the expected remaining lifetime of the recipient. This means that the total amount of benefits paid out will be the same, regardless of whether they are paid out monthly or at some other interval.

For example, let's say that a retiree is entitled to receive $1,000 per month in pension benefits. If the retiree is expected to live for another 20 years, the actuarial equivalent of this benefit would be $240,000 ($1,000 x 12 months x 20 years). This means that if the retiree chooses to receive a lump sum payment instead of monthly payments, the lump sum payment would be $240,000.

Another example would be if a retiree is entitled to receive $500 per month in pension benefits, but they choose to receive payments every three months instead of monthly. In this case, the actuarial equivalent of the benefit would be $1,500 ($500 x 3 months), which is the same total amount of benefits paid out over the expected remaining lifetime of the recipient.

These examples illustrate how the actuarial equivalent ensures that the total amount of pension benefits paid out is the same, regardless of the payment frequency or method chosen by the recipient.