Rule. Divide the amount by the annuity, and multiply the quotient 
by 8 times the interest of £l for one year; add to this the square of the 
difference between 2, and the interest of £l for a year, and extract the 
square root of the sum ; from this result subtract the difference between 
2 and the interest of £ 1 for a year, and divide by twice the interest of 
£l for one year. 
Example. How many years must an annuity of £325 be forborne 
to amount at 3^ per cent simple interest to £4650 15 0? 
a ~ 325 
s = 4650.15 
325)4650.15 ( 14.31 = 
1400 
1300 
1001 
915 
.325 
325 
11448 
2862 
4.0068 = 
2. 
.035 
1.965 = 2 — i 
1.965 
9825 
11190 
11685 
1965 
.01 = 2i 
(2 - if = 3.861225 
8 i —= 4.0068 
a 
8 _ + (2 - iy 1.868025(2.805 = V 8z— + (2 
4. 1.965 = 2 - i 
48)386 .07).840=\/8t ~ +(2—¿Y—(2 — 0 
12 years 
divid 
Ru 
years 
by the 
one. 
Exc 
£325 
325)46 
18. I 
done by 
sum of 
If we 
pression 
For 
covei 
a Ion 
ever, 
low’s