32 
ON THE VALUE OF ANNUITIES. 
Taking the last example; under the 5 per cent column opposite 
12 years we have 15.917127 
this multiplied by the annuity. . 76613.03 
47751381 
477514 
15917 
9550 
955 
m 
482.55428 = £482 11 1 as before. 
Example. What will be the amount of an annuity of £325 in 9 years 
at £3 6 per cent compound interest ? 
i = .033 a - 325 n = 9 
log (1+0 = log 1.033 =0.01410032 
9 
log 1.033 9 = 0.12690288 1.339377 
.339377 
523 
"1018131 
67875 
16969 
.033)110.2975 
3342.348 = £3342 7] 
nearly. ) 
Suppose a sinking fund of £1,000,000 per annum is put by towards 
the redemption of the national debt for 50 years; what portion of it will 
be discharged at the expiration of that period, assuming the interest of 
money at 3^- per cent ? 
By Table 5, the amount of £l per annum in 50 years at 3i per cent 
is 130.997910, which multiplied by 1,000,000 gives £130,997,910. 
This calculation is made on the supposition that all the dividends 
which would have been due on the redeemed stock, are added each year 
to the million, and laid out in the purchase of stock to be cancelled. 
46. To find («) the annuity. 
Art. 44, s = a 
(1 + i) n - 1 
i 
dividing each side by — v 
a = 
(i + 0" - 1 
Buie. Multiply the amount of the annuity by the interest of £l for 
one year, and divide the product by the amount of £l in the given time, 
less one.