6.-Survivorships.

Prefatory remarks to survivorships; LXXIX. To find-1. the present value, in a

single payment, of a given annuity, to be entered upon by a given life, at the

death of another given life-2. the same, in annual payments-3. what annuity

a given sum will purchase, during a given life, after the death of another given

life; LXXX. To find the value, after the life in possession, of the next inhe-

ritance to an annuity-1. during a succeeding life-2. during the joint existence

of two succeeding lives-3. during the last survivor of two succeeding lives;

LXXXI. To find-1. The value of an annuity, held during a given life, and

also, afterwards-1. during another single life; or 2. during two joint lives; or

3. during the last survivor of two lives, each and all to be appointed at the death

of the existing life-2. the value of an annuity during the existing life, and

afterwards for a term of years certain; LXXXII. 1. To find the value of a

perpetuity after the failure-1. of a single life; 2. of two joint lives; and

3. of the last of two lives-2. To find the value of what may remain of an

annuity for a number of years certain after the failure-1. of an existing

life; 2. of two joint lives; or 3. of the last of two lives; LXXXIII. To

find the value of an annuity certain for a given number of years, and after-

wards to continue-1. during an existing life-2. during two joint lives-or 3.

during the last of two lives; LXXXIV. 1. To find the value of an annuity to be

divided equally between two persons during their joint lives, and to be reduced

one half during the life of the survivor-2. To find what annuity a given sum

will purchase which is to be divided equally between two persons during their

joint lives, and then to be reduced one half during the life of the survivor;

LXXXV. 1. To find what sum each of two persons ought respectively to pay

for an annuity, to be equally divided between them while both are alive, and on
the death of either to belong entirely to the survivor-2. To find the value of
that part of an annuity granted on the longest of two lives, which, on the death
of either of them, is to continue during the life of the survivor:

Assurances-LXXXVI. 1. To find what premium, in a single payment, will

assure a given sum at the death of a given life, provided another person be then

alive-2. The same, in annual payments.

7.-Practical examples.

DECIMALS.

The pupil is, for his own sake, earnestly recommended to perfect himself in decimals, in order that he may proceed with certainty and success, to acquire a thorough knowledge of the important subjects embraced in the following pages.

ABBREVIATIONS.

For the sake of brevity, the usual symbols will be adopted; namely,
for Equality.

+ for Addition.

for Subtraction.

x for Multiplication.

for Division.

REFERENCES.

Whenever the Roman numbers, I., II., III., IV., &c., are placed in a sentence, or in an operation, a reference is intended to that part of the work where the subject is more fully explained.

The same Roman numbers, followed by a figure, imply a similar reference; the figure shewing only the particular division of the subject.