31

will earn 4 per cent. interest per annum until required to be used.

For convenience let us assume that we have 100,000 such insurances starting at the same moment, each for $1,000 and each on a life aged To. Then there y ill be 10o,000 insured ahogether for one year. According to this table 676 persons out of the 100,000 will die during that rear, calling for $676,00o to be paid at the end of the rear. The sum which mist be on hand at the beginning of the year to meet payments of 5676,000 at the end of the year, d per cent, interest being realized, is $676,000 - I.04 _ $(')50.000. If each of the 100,000 persons insured pays his quota of this sum he will pay a premium for the rear, in advance, of $6.5o for his $Logo insurance.

The same resuh may be reached thus : The share of each in paving the total losses of $676,00o is $6.76 for his $1,000. But this would not need to be paid until the end of the year—in which case the premiums of those who had died could be deducted from the amounts of their insurance—and, since it is paid at the beginning of the rear, it must be discounted at 4 per cent. and becomes $6.7(i - 1.04 _ $6.;0, as before.

Or, in a more general way, it may be reached thus: The risk of death for each is 1- 6713

This would be

the premium payable at the end of the year for an insurance of 1 ; the premium payable at the beginning of the year for an insurance of 1 is   'u 4 — I U 6 U °

111pUU~   ].-UU07

and the premium payable at the beginning of the year

for an insurance of S~I,000 is "s — X $i,000 = $6.50,

as before.