ADDITION TO CHAPTER X.
The following formulae will sometimes be found useful.'1 if the party die in the first year, X2 if in the second, and so on, is —
1+A—rI
1+r
where A is the value of a common annuity ; I that of an annuity which is '1 at the first payment, X2 at the second, and so on; and r the interest of X1 for one year.
If an office engage to pay 1 at the death of an individual, and also to return all the premiums at the same time, that is, if they guarantee that the interest of his investments shall amount to '1, the premium which should be demanded is
E—A
1+A+I
where A and I are as before, and E is the value of a perpetuity of '1.