To find what annuity, or sinking fund, will amount to a given sum

This merely reverses the problem of Formula VI. If an annuity of one
dollar will amount to n, the desired number of dollars divided by n will
show the number of dollars in the annuity desired.

To find what investment will buy a given annuity

This is simply the problem of the present worth of an annuity. Since,
by Formula VII,

To find what annuity a given sum will buy

This, too, is a problem in the present worth of an annuity. Here our
given sum, or P, is the same as the present worth, or M of Formula VII.
If the present worth of an annuity of one dollar is m, the present worth of
the unknown sum will be P divided by m.

To find the yield of a bond purchased at a given price

As was stated in Chapter XII, no method has been discovered for find-
ing in all cases the exact yield of a bond by figuring backward from the
known price--unless a rate of interest on assumed reinvestments is to be
taken for granted. To assume a rate on reinvestments different from that
on the principal is obviously to put aside the thing one is trying to learn.
By such a process a part of the yield of the investment is made to depend
on the rate arbitrarily chosen for reinvestments. Even when this method
is used for purposes of comparison it is misleading if the ratios of reinvest-
ment to principal are different in the two cases. What an investor really
wishes to know is usually the rate paid on investments of this class; and
that assumes returned premium to be either reinvested in securities of the
same class or else not reinvested at all. The only method of determining

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