First off, may your father rest in peace!
Next, a question jumps out, but also may be heading into privacy issues, so forgive me for asking.
Is that 40% only for a one-off payment normal in the state or nation where your father lived, that has control over such matters?
I sure don't have any legal expertise in such matters, but it seems really weird. Where does that 60% go? Well that is another loaded question and maybe neither should be answered so we don't head into private matters at your end. But my goodness, 60% is one heck of a cut for some entity!
The 60% hasn't gone anywhere.
For round numbers, assume the supposed 'full value' is $10,000, and so vs the long term payments, the immediate worth would be $4,000 (=40%).
Plug $4,000 into a compounding calculator at 5%/yr, and after 20yrs you'll have a little over $10,000 ($10,613). The insurance company that sold the annuity is betting that they can make more than 5%yr on the money, and they'll pay the beneficiary a set amount each year, and keep the rest (which is their business model).
The long term return in the stock market is more like 7%, and at that rate, $4,000 becomes $15,478 after 20 years. This would be more than enough to pay a client 5%/yr, (totaling $10,000 at the end) and still make some profit.
That's the game, the business. The client gets a guaranteed payment over a set term (no risk), and the insurance company assumes the risk (and variation in returns over the years), and of course hopes that they will come out with some profit in the end. Usually, large insurance companies are safe in terms of risk, but there is a small chance of them going bankrupt--in which case the payments would stop (so one aspect of the choice is--is the insurance company solid financially).
So the choice is (a) take the $4,000 now and invest it, taking on the investment risk on your own, or (b) let the insurance company take the risk for a slightly lower total payout.
There are tax considerations for either choice--initial tax on the lump sum vs ongoing tax on yearly payments. Possible taxes on investment returns if you do it on your own. Also, maybe there is a high-interest debt that could be paid off immediately with the lump sum, which is also a kind of guaranteed return. Inflation would effectively shrink the yearly payments by, you guessed it--the rate of inflation. At 2% inflation, in year 20 you'd need about $1500 to get the same 'value' as $1000 in year 1.
Lots of things to consider and wonder about.