A 25-year-old person entered into a contract with an insurance company, which would pay 10,000 francs to their family in the event of their death, obligating themselves to pay a premium of 450 francs semi-annually in advance. At what age did they die if the insurance company lost 1000 francs when paying out the insured amount?
If the number of half-years is $n$, then according to the problem:

$$
450 q^{n}+450 q^{n-1}+\ldots+450 q=9000
$$

or

$$
450 g \frac{q^{n-1}}{q-1}=9000
$$

if $p=5\%$, then $q=1.025$ and $n=16$; hence, the person lived for another 8 years.

The problem was solved by: Krausz B., Krisztián Gy., Pollák N., Sasvári G.