$3.$ A life insurance company issues a special $2-$payment whole life assurance to

lives aged $60$ exact. The death benefit is paid at the end of the year of death.

Premiums of P are paid at the beginning of years $1$ and $3.$ If a life aged

$60$ dies in either year $1$ or year $3,$ the death benefit is e $15,000+$ P

$4($partial

refund of premium$).$ Otherwise the death benefit is e $15,000.$ Calculate P $.$

Basis:

Mortality: AM$92$ Ultimate

Interest: $4\%$ per annum