Interest for the kth year
= Pi (1 + 1 - k n).
Total amount of interest to the end of the kth year
= Pik (1 + 1 - k 2n).
Total amount of interest and principal paid up to the end of the kth year
= Pk (1 n + i (1 + 1 - k 2n)).
The following table shows how a debt of $10,000 bearing 5 per cent interest would be discharged by equal annual payments in five years:
| Year | Principal at Beginning of Year | Interest for Year | Principal Repaid at end of Year | Total Annual Payment |
|---|---|---|---|---|
| 1 | $10,000 | $500 | $2,000 | $2,500 |
| 2 | 8,000 | 400 | 2,000 | 2,400 |
| 3 | 6,000 | 300 | 2,000 | 2,300 |
| 4 | 4,000 | 200 | 2,000 | 2,200 |
| 5 | 2,000 | 100 | 2,000 | 2,100 |
| Totals | $1,500 | $10,000 | $11,500 |
Annuity Bonds are those wherein a uniform periodic payment is made to discharge the debt in a given time. The formula for the necessary payment to discharge a debt of P, with interest rate i in n years is,
Annual payment = i 1 - (1 - i)-n . P.