The formula to calculate the Annual Percentage Yield is:
\[ \text{APY} = \left(1 + \frac{r}{nc}\right)^{nc} - 1 \]
Where:
Annual Percentage Yield is a normalized representation of an interest rate, based on a compounding period of one year.
Let's assume the following values:
Using the formula:
\[ \text{APY} = \left(1 + \frac{5}{10}\right)^{10} - 1 \]
Evaluating:
\[ \text{APY} = \left(1 + 0.5\right)^{10} - 1 \]
\[ \text{APY} = 1.5^{10} - 1 \]
\[ \text{APY} = 56.6650390625 \]
The Annual Percentage Yield is approximately 56.6650390625%.
| Stated Annual Interest Rate (%) | Compounding Periods | Annual Percentage Yield (%) |
|---|---|---|
| 1 | 1 | 100.000000000000 |
| 1 | 2 | 125.000000000000 |
| 1 | 3 | 137.037037037037 |
| 1 | 4 | 144.140625000000 |
| 1 | 5 | 148.832000000000 |
| 1 | 6 | 152.162637174211 |
| 1 | 7 | 154.649969704071 |
| 1 | 8 | 156.578451395035 |
| 1 | 9 | 158.117479171320 |
| 1 | 10 | 159.374246010000 |
| 1 | 11 | 160.419901189753 |
| 1 | 12 | 161.303529022468 |
| 2 | 1 | 200.000000000000 |
| 2 | 2 | 300.000000000000 |
| 2 | 3 | 362.962962962963 |
| 2 | 4 | 406.250000000000 |
| 2 | 5 | 437.824000000000 |
| 2 | 6 | 461.865569272977 |
| 2 | 7 | 480.779509995228 |
| 2 | 8 | 496.046447753906 |
| 2 | 9 | 508.627514018754 |
| 2 | 10 | 519.173642240000 |
| 2 | 11 | 528.141285002137 |
| 2 | 12 | 535.859955866530 |
| 3 | 1 | 300.000000000000 |
| 3 | 2 | 525.000000000000 |
| 3 | 3 | 700.000000000000 |
| 3 | 4 | 837.890625000000 |
| 3 | 5 | 948.576000000000 |
| 3 | 6 | 1,039.062500000000 |
| 3 | 7 | 1,114.265678902013 |
| 3 | 8 | 1,177.678495645523 |
| 3 | 9 | 1,231.829497535944 |
| 3 | 10 | 1,278.584918490001 |
| 3 | 11 | 1,319.347887519562 |
| 3 | 12 | 1,355.191522836685 |
| 4 | 1 | 400.000000000000 |
| 4 | 2 | 800.000000000000 |
| 4 | 3 | 1,170.370370370370 |
| 4 | 4 | 1,500.000000000000 |
| 4 | 5 | 1,789.568000000000 |
| 4 | 6 | 2,043.347050754457 |
| 4 | 7 | 2,266.260292419461 |
| 4 | 8 | 2,462.890625000000 |
| 4 | 9 | 2,637.206646032600 |
| 4 | 10 | 2,792.546549759998 |
| 4 | 11 | 2,931.686660714370 |
| 4 | 12 | 3,056.929179344459 |
| 5 | 1 | 500.000000000000 |
| 5 | 2 | 1,125.000000000000 |
| 5 | 3 | 1,796.296296296297 |
| 5 | 4 | 2,462.890625000000 |
| 5 | 5 | 3,100.000000000000 |
| 5 | 6 | 3,697.070044581621 |
| 5 | 7 | 4,250.933466740658 |
| 5 | 8 | 4,762.133985757828 |
| 5 | 9 | 5,232.977312926782 |
| 5 | 10 | 5,666.503906250000 |
| 5 | 11 | 6,065.953887109499 |
| 5 | 12 | 6,434.496113081846 |
| 6 | 1 | 600.000000000000 |
| 6 | 2 | 1,500.000000000000 |
| 6 | 3 | 2,600.000000000000 |
| 6 | 4 | 3,806.250000000000 |
| 6 | 5 | 5,053.632000000001 |
| 6 | 6 | 6,300.000000000000 |
| 6 | 7 | 7,519.337059509948 |
| 6 | 8 | 8,696.388244628906 |
| 6 | 9 | 9,822.903012752113 |
| 6 | 10 | 10,895.116277760006 |
| 6 | 11 | 11,912.090579484224 |
| 6 | 12 | 12,874.633789062500 |
| 7 | 1 | 700.000000000000 |
| 7 | 2 | 1,925.000000000000 |
| 7 | 3 | 3,603.703703703704 |
| 7 | 4 | 5,619.140625000000 |
| 7 | 5 | 7,862.623999999998 |
| 7 | 6 | 10,245.526834705084 |
| 7 | 7 | 12,700.000000000000 |
| 7 | 8 | 15,176.018530130386 |
| 7 | 9 | 17,637.698105068459 |
| 7 | 10 | 20,059.939004489992 |
| 7 | 11 | 22,425.685662139236 |
| 7 | 12 | 24,723.799730734198 |
| 8 | 1 | 800.000000000000 |
| 8 | 2 | 2,400.000000000000 |
| 8 | 3 | 4,829.629629629629 |
| 8 | 4 | 8,000.000000000000 |
| 8 | 5 | 11,781.376000000002 |
| 8 | 6 | 16,038.408779149506 |
| 8 | 7 | 20,646.867498114851 |
| 8 | 8 | 25,500.000000000000 |
| 8 | 9 | 30,509.603741685423 |
| 8 | 10 | 35,604.672266240013 |
| 8 | 11 | 40,729.125092833769 |
| 8 | 12 | 45,839.365799778287 |
| 9 | 1 | 900.000000000000 |
| 9 | 2 | 2,925.000000000000 |
| 9 | 3 | 6,300.000000000000 |
| 9 | 4 | 11,056.640625000000 |
| 9 | 5 | 17,110.367999999995 |
| 9 | 6 | 24,314.062500000000 |
| 9 | 7 | 32,495.196122121117 |
| 9 | 8 | 41,478.754431009293 |
| 9 | 9 | 51,100.000000000000 |
| 9 | 10 | 61,210.662578009978 |
| 9 | 11 | 71,681.150613789257 |
| 9 | 12 | 82,400.500684976578 |
| 10 | 1 | 1,000.000000000000 |
| 10 | 2 | 3,500.000000000000 |
| 10 | 3 | 8,037.037037037041 |
| 10 | 4 | 14,906.250000000000 |
| 10 | 5 | 24,200.000000000000 |
| 10 | 6 | 35,859.396433470531 |
| 10 | 7 | 49,726.016735009624 |
| 10 | 8 | 65,584.083557128906 |
| 10 | 9 | 83,191.335110312168 |
| 10 | 10 | 102,300.000000000000 |
| 10 | 11 | 122,670.127065638662 |
| 10 | 12 | 144,077.409234590683 |