TEMPORARY ANNUITIES, 
127 
Rule. From the value of an annuity for the -whole term of life, sub 
tract the value of an annuity deferred for the number of years which 
the temporary annuity has to continue; the difference will be the 
required value of the temporary annuity. 
138. By Davies’s method 
N N N -N 
— - - (Art. 112 and 136.) 
Rule. From the number in column N opposite the present age, 
subtract the number in column N opposite the age at which the annuity 
will cease, and divide the difference by the number in column D oppo 
site the present age. 
139. The present value of an annuity for n years, payable at the 
beginning of each year, will be unity added to the present value of an 
annuity for (?i — 1) years, payable at the end of each year, i. e. 
D,+ N,-N 
the quantity D m + N„ being, by the construction of the tables, equal to 
Similarly, the present value of £l paid down, and of an annuity of £l 
for n years payable at the end of each year, will be 
140. To find what annual premium should be paid in lieu of a gross 
sum to secure a deferred annuity. 
When a reversionary annuity is secured by an annual premium the 
first payment is usually made immediately, and the subsequent payments 
at the end of each year until the reversion is entered upon. 
As the present value of an annuity of £l for the term increased by 
one year’s purchase, is to £l, so is the present value of any other sum 
to the equivalent annual premium. 
1 ei m u 
or 
annual premium.'