50 
ON THE VALUE OF ANNUITIES. 
Tableé, (1.03)- 9 = .166411 = (I + ¿') _Cd + 0 
8 
67Í31336 = d (1 + i') - (d + 1) 
6.45114 
12.58301 = - + d (1 +¿ , )~( d + 1 > 
a 
Tableé, 1.03- 19 = .510286= (1 + 
81 
510286 
456229 
10726515 = (d + n) (1 + 
12.58301 
"2731192 =£+d(l+fr W) -(d+ra) (l+¿'r (J+n+,) 
Cl 
2.318).008462(.0036 = z 
6954 
1508 
i = i' + 2 = .0336, which on trial will be found extremely near 
the true value, which is .0333. 
64. When the reversion is in 'perpetuity, (1+0 (d + n) in’ the for 
mula of Art. 59. vanishes, and the equation becomes 
, _ a{ 1 + i)~ d 
^ i 
Rule. Multiply the present value of £l, due the number of years the 
perpetuity is deferred, by the annuity, and divide by the annual interest 
of ¿£1. 
Example. What is the present value of the reversion of a perpetuity 
of ,£50 per annum after 10 years, at 5 per cent interest ? 
ti — 50 d ~ 10 i — .05. 
Tableé, (1 + i)~ d = (1.05)- 10 =.613913 
_50 = a 
.05)30.69565 
613.913 = £613 18 3. 
65. 
To find (a) the annuity. 
Art. 64. p ~ 
q(i + 0~l 
multiplying by i and dividing by (1 + i)~ d 
a 
ip 
= ip (1 + o d • 
Rule. Multiply the present value of the reversion by the annual 
interest of £l and hy the amount of £l at the end of the term the per 
petuity is deferred.