S = .04 (1 + .04)5 - 1.$10,000
To solve, the denominator is first evaluated:
| Log (1 + .04)5 | = | 5 log 1.04 |
| = | 5 × 0.017033 | |
| = | 0.085165 |
Taking the antilog,
(1 + .04)5 = 1.21665
and
(1 + .04)5 - 1 = 0.21665
Then
S = 0.4 × $10,000 0.21665 = $1846.27.
Annuity tables, which may be seen at nearly any bank or brokers’ office, or in Bulletin 136, U. S. Department of Agriculture, give the annuity which will amount to 1 in five years at 4 per cent as 0.1846271; this multiplied by $10,000 gives $1846.27.