$.(28),(29)$ and $(30)$ take out a policy that will pay an insured sum of $$3,000,000$ if at least two of the three people die within a $20-$year period. Additionally, a growing life annuity is offered to the last survivor of the group, starting with $$50,000$ the first year $(*),$ $$100,000$ the second year $(*),$ $$150,000$ the third year $(*)$ and so on until you die. The premiums are payable every $3$ months while all persons are alive. $(*)$ The years are counted from this moment $($for example, if the third death occurs in the $12$th year, the first annuity payment for the last survivor will be of $$600,000$ in year $12)$ Using table $1,$ a rate of i$=5\mathrm{.}9\%,$ calculate and write the notation: a$)$ Calculate and give the notation for the calculation of the PNU b$)$ Reserve at the end of year $10($Assuming $(28)$ died$)$ c$)$ Reserve at the beginning of year $3($All alive$)$ d$)$ Reserve at the end of year $5($All alive$)$