Annuity: $2B paid monthly over 30 years is $5.5M/month; $3.5M after taxes.
Lump sum: $1B, $670M after taxes. Invested in index fund at, say 8%, can be expected to earn $4.5M/month, $3.6M after more taxes, which are lower for capital gains & dividends.
There’s more complicated maths, if you want to model taxes, future values, and variable market returns, but they all say pretty much the same thing. They have to: the annuity works because They put the lump sum into escrow, pay a trustee to manage it well enough to pay the annuity and pay the trustee’s salary. That means the trustee will invest said lump sum (before taxes) in low-risk, low-return assets, take his vig, and pay out the annuity from what’s left.
The usual math goes something like
Annuity: $2B paid monthly over 30 years is $5.5M/month; $3.5M after taxes.
Lump sum: $1B, $670M after taxes. Invested in index fund at, say 8%, can be expected to earn $4.5M/month, $3.6M after more taxes, which are lower for capital gains & dividends.
There’s more complicated maths, if you want to model taxes, future values, and variable market returns, but they all say pretty much the same thing. They have to: the annuity works because They put the lump sum into escrow, pay a trustee to manage it well enough to pay the annuity and pay the trustee’s salary. That means the trustee will invest said lump sum (before taxes) in low-risk, low-return assets, take his vig, and pay out the annuity from what’s left.