74   Life Contingencies

10. For a joint life assurance with annual premiums we have nl7xy=Ax+n:y+n—Pxy.ax+n:y+n.

For a survivorship assurance with annual premiums payable during the duration of the contract we have, if both lives have survived n years.

n Vxy —Ax +n : y+n —Pxy ax+n :Y+n

But if x alone has died within the n years, the reserve at the end of n years, is Ay+n —Pxy ay+n.