Q

$10.$ On $1$ January $2006,$ an insurance company issued a whole life policy to a life aged $45$ exact. The sum insured on the policy is $$120,000$ which is payable at the end of the year of death. Level premiums are payable annually in advance until age $65$ or earlier death. The company calculated the premium on the following basis:

$\backslash$table$[[$Mortality:$,$AM$92$ Select$],[$Interest:$,6\%$ per annual$],[$Initial expenses:,$75\%$ of the first year's premium, incurred at time $0],[$Renewal expenses:,$5\%$ of the second and each subsequent year's premium,$],[,$incurred at the beginning of the respective policy years$],[$Claims expense:,$$300$ payable at the end of the year of death$]]$

$($i$)$ Calculate the annual premium.

On $31$ December $2020,$ immediately before the premium due for next year, the life wishes to surrender the policy. The insurance company calculates a surrender value equal to the gross policy value, using the following basis:

Mortality: AM$92$ Ultimate

Interest: $,6\%$ per annual

Expenses: Ignore

$($ii$)$ Calculate the surrender value payable by the insurance company.T