To the nearest cent the following tabular statement shows the growth of the sinking funds:
| Year | Sinking- fund at Beginning of Year | Interest during Year | Annual Payments into Sinking- Fund | Total Sinking- fund at End of Year | ||||
|---|---|---|---|---|---|---|---|---|
| 1 | 0. | 0. | $1,846. | 27 | $1,846. | 27 | ||
| 2 | $1846. | 27 | $73. | 85 | 1,846. | 27 | 3,766. | 39 |
| 3 | 3766. | 39 | 150. | 66 | 1,846. | 27 | 5,763. | 32 |
| 4 | 5763. | 32 | 230. | 53 | 1,846. | 27 | 7,840. | 12 |
| 5 | 7840. | 12 | 313. | 61 | 1,846. | 27 | 10,000. | 00 |
If this loan, the bonds, bore 5 per cent interest the cost to the borrower would have been the principal plus the interest on principal less the interest on the sinking fund:
$10,000 + $2500 - $768.65 = $11,731.35;
or the interest on the loan plus the sinking-fund payments:
$2500 + $9231.25 = $11,731.35
Serial Bonds are such that a fixed amount of the principal is retired at definite periods of time. Usually the amount retired is an aliquot part of the whole. The payments to be made at any particular time is the fixed portion of the principal plus the interest on the unpaid portion up to that date. The periods of retirement are usually annual or semi-annual.
Assuming the principal to be P and that one nth part of it is paid each year, the formulas are:
Annual payment for the kth year
= P ( 1n + i (1 + 1 - k n)).