# How are annuity rates calculated for money purchase/DC pensions?

I have two pension schemes from two different UK major providers, and they are presumably using whatever the legal requirements are for calculating projected annuity for my pot, but to me they seem exceptionally conservative.

Basically, both companies' statements say at retirement age of 65 they project my value to be (my rounding) £100,000, giving an annuity of about £3,000. To my untrained eye, assuming zero effective growth, this looks like they are projecting I live to around 95 years old, which whilst desirable is way above the expected average. Furthermore, they state that they are projecting on inflation of 2.5% (I presume the annuity payout would grow by this amount per year?) and a fund growth of 4.5%, so the funds backing my annuity should be growing by 2% (minus fees) per year.

How are these figures arrived at? Are they deliberately (by law?) pessimistic or am I missing something in my simplistic calculations.

• There are two things here: the way they are projecting the growth of the current portfolio up to the date of retirement - there are indeed rules for how they do this; and the calculation they are making for how a given pot might translate into annuity income - this will (I expect) be based on the actual current annuity rates available, which indeed are that bad. Will give a longer answer if you can clarify if it's the growth or the annuity rate you're interested in Mar 15, 2021 at 10:51
• It's the annuity rates I'm interested in - on the face of it, taking a lump-sum and investing directly in an index-linked fund seems so much better. Is there information out there about how annuity rates change over time? EDIT I just found this table that shows rates going down the toilet... Mar 16, 2021 at 0:15

This isn't necessarily how your UK providers calculate your annuities, but it might help on your 30 year drawdown projection.

If the £3000 annual annuity is based on today's value, and you expect to retire in 30 years, £100k would last about 20 years according to my calculation based on my answer here.

The main difference is due to the inflation-linked withdrawals starting at ~£6300. (If they actually start at £3000 I calculate the drawdown period could last 57 years.)

(Copying the structure of my previous answer)

For the scenario below, a pension pot is calculated to deliver inflation-linked withdrawals relative to today.

``````                               Time (year)
Today          March 2021          0
Living it up   March 2051         30        first pension withdrawal (no. 1)
All done       March 2070         49        last pension withdrawal (no. 20)
``````

With

``````i = annual inflation
m = annual stock market gain
o = year number of first withdrawal
n = number of withdrawals
w = withdrawal amount (in today's value)
p = pension pot upon retirement

i = 0.025
m = 0.045
o = 30
n = 20
w = £3000

p = ((1 + i)^o (1 + m)^-n ((1 + i)^n - (1 + m)^n) w)/(i - m) = £100,859
``````

(p is the pot in March 2050, so it does grow prior to the 1st withdrawal)

The first inflation-linked withdrawal is `w (1 + i)^30 = £6292.70`

and the pension pot is drawn down to zero in March 2070.

Based on calculations here

£100,000, giving an annuity of about £3,000.

Take a look at this news article from 2013, which describes these factors behind the trend of declining annuity rates:

Long-term factors, such as increasing life expectancy are behind the trend but more recently low interest rates and falling gilt yields, exacerbated in part by quantitative easing, have speeded the downward slide.

The systemic trends described there have only continued since. The idea of getting 15%, as you apparently could in 1990, now seems in the realm of the absurd.

You'd think the fact that annuitising is no longer compulsory would work to make them more competitive products, but life expentancy trends are too significant for that to make a dent.