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$7.$ Understanding universal life insurance

Universal life insurance combines elements from term life insurance and whole life insurance. Term policies provide a death benefit

$q,$ savings component, whole life policies provide a death benefit $$ savings component, and universal policies provide a death benefit $$ savings component. To understand how universal premiums are allocated, consider the following example.

Eric is a $41-$year$-$old lawyer who has taken out a universal life insurance policy to protect his two children $($ages $12$ and $9)$ in the event of death. Each year, Eric chooses how much would like to contribute to the policy, as shown by the first row of the table below. The insurance company subtracts from this an administrative fee along with the cost of the death benefit $($the $$ portion of the policy$)$ then puts the remainder into the cash value $($or $)$ portion of the policy. This money earns interest at a $q,$ rate of return. Based on the given information, calculate the amount that is added to the cash value portion of the policy in each of the first three years.

$\backslash$table$[[,$Year $1,$Year $2,$Year $3],[$Premium $($annual contribution$),$$$2,834,$$$2,220,$$$1,757$