ENDOWMENTS. 
135 
P(m, n *' C^m+n 4" m^n ) 
tm+n htty+n 
lm • lm. 
• f C^ni+it 4“ ^m 1 +n m^+it ) • 
What is the present value of an annuity of £50 deferred 10 years, 
and then to continue until the death of the survivor of two males, now 
aged 35 and 40 years ? (Chester 3 per cent.) 
' - , ^45 in * ho 10 hb • ho n 
fl O») ll0 +»W 110 “ a C35.40). 10 r i0 +a M r 10 - «45.50 . J-J- T X 
I 1 A *35 *40 ^35 •¿40 
log «4 5 = log. 14.3812 rr 1.1577951 
log /45= log 4116 = 3.6144754 
ar. co log. ¿ 35 =ar. co log 4849 = 4.3143478 
logr l0 = logl.OS“ 10 = 1.8716278 
0.9582461 9.083 
log «50= 
log 13.0950 = 1.1161055 
log ho= 
log 3675 = 3.5652573 
log Z 40 = ar. co 
log 4516 = 4.3452461 
C 
aq 
0 
11 
log- 1.01- 10 = 1.8716278 
0.8982367 7.911 
log ^45.50 
log 9.823 0.9922441 
l0g ¿45 “ 
log. ¿35 +log r 10 =; 1.8004510 
lOg ¿50 — 
log ¿40 = 1.9105034 
0.7031985 5,049 
9.083— a (35) 11() 
7.911= «(40) llo 
16.994 
5.049 = «(35.40) 110 
11.945 
50 
59T.25 = £597 5 0. 
What is the present value of £50 per annum, to he entered upon at 
the end of 10 years, provided two males, now aged 35 and 40, shall 
jointly survive that period, and then to continue until the death of the 
last survivor ? (Chester 3 per cent.)