THE THEORY OF INTEREST

the number of j’s being n(m — 1)

it

t(

tt

it

“ x’s ““ i’s “

mnm — 1

making a total of 2mn + m — n — 1 carried forwardfrom the first approximation.

In addition, the new unknowns, the y’s and the r’s, areintroduced. There is one y for each individual for eachyear, the total array of y’s being

Vi, v",- • • ,yi m) ,y/, y",---,y* m \

y», y",- • -,yn m) -

The number of these y’s is evidently mn.

There is one r for each individual for each pair of suc-cessive years, i.e., first-and-second, second-and-third, etc.,and next-to-last-and-last years, the total array of r’s being

r / T rr T (m—1)

•!)•! y • • y • 1 >

T r T rt „ (m—1)

•2 > •2 } * • j * 2 ?

The number of these r’s is evidently n(m — 1).

In all, then, the number of new unknowns, additionalto the number of old unknowns carried forward from thefirst approximation, is mn -(- n(m — 1), or 2mn — n.Hence we have:

number of old unknowns, 2 mn + m — n — 1,

+ number of new unknowns, 2 mn — n,

= total number of unknowns, 4 mn + m — 2n — 1,

as compared with 3 mn + m — n equations.

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