A whole life assurance is sold to a life aged 45.

Level premiums equal to P per annum are paid yearly in advance for the entire contract duration, ceasing on death. The following benefits are paid under the contract:

in case of death during the first 5 years, a benefit equal to 5 P is paid at the end of the year of death.

in case of death between the 5th and 10th year,a benefit equalto10P is paid at the end of the year of death.

after the 10th year, the death benefit is 150 000, payable at the end of the year of death.

interest rate i = 3% are used as valuation basis for both premium and provision.

1. Write an expression for the PV of future loss tL at any (integer) duration t.