This paper examines the contract of a policyholder who has a profit-sharing contract starting from January 2014, i.e. t = 0, with an insured amount of 1000 euros. The contract states that for each year the company makes a profit of 3% or more, its insured amount will increase. The increase in the insured amount depends on the value of 0.75 max(R − 0.03), where R is the rate of return the company made that year. It is already known that the policyholder will pass away in exactly 50 years. Keeping this information in mind, it is possible to calculate the value of the insured amount at the end of the contract.
To calculate the problem at hand, this paper first examines the available data. Then it establishes a solid theoretical background. Subsequently, the methods which enable us to tackle this problem are elaborated upon. Afterwards, a practical application is introduced. Finally, the approximation methods are discussed and the outcomes are evaluated.