According to the article below, health insurers typically use 80-85% of premiums to pay out claims. I didn't find anything for life insurers, but that's probably good enough. I'll choose 85%, which means the profit would be 15%. This would cover administrative costs plus their actual profit.
So, if they sell 100,000 premiums, they would need that revenue to cover 47 * 50,000 = $2,679,000 in pay outs.
To cover their profits/admin expenses, etc. they need to make more than that. Assume that $2,679,000 is 85% of what they need to make.
0.85x = $2,679,000
x = $3,151,765
So for 100,000 premiums the price per premium is:
$3,151,765/100,000 = $31.52 <--------------ANNUAL PREMIUM is $31.52
Amount of profit:
$3,151,765 - $2,679,000 = $472,765 <-----------ANNUAL PROFIT is $472,765
