I couldn't sleep last night and ended up wondering if you'd make more money over 15 years if you made 1% interest the first year up to 15% on the last year or vice versa, making 15% the first year and 1% the last.
So my gut tells me that making 15% the first year will yield more money as you're making interest on a larger amount (after the first year) and compound interest loves time.
Maybe you'll end up with same at the end but I can't imagine having an incrementing interest rate will yield more than a decrementing one.
To the spreadsheets!
So assuming my math is right here's the resulting table.
| % | Amount | Total | % | Amount | Total |
|---|---|---|---|---|---|
| 0% | $0.00 | $1,000.00 | 0% | $0.00 | $1,000.00 |
| 1% | $10.00 | $1,010.00 | 15% | $150.00 | $1,150.00 |
| 2% | $20.20 | $1,030.20 | 14% | $161.00 | $1,311.00 |
| 3% | $30.91 | $1,061.11 | 13% | $170.43 | $1,481.43 |
| 4% | $42.44 | $1,103.55 | 12% | $177.77 | $1,659.20 |
| 5% | $55.18 | $1,158.73 | 11% | $182.51 | $1,841.71 |
| 6% | $69.52 | $1,228.25 | 10% | $184.17 | $2,025.89 |
| 7% | $85.98 | $1,314.23 | 9% | $182.33 | $2,208.21 |
| 8% | $105.14 | $1,419.37 | 8% | $176.66 | $2,384.87 |
| 9% | $127.74 | $1,547.11 | 7% | $166.94 | $2,551.81 |
| 10% | $154.71 | $1,701.82 | 6% | $153.11 | $2,704.92 |
| 11% | $187.20 | $1,889.02 | 5% | $135.25 | $2,840.17 |
| 12% | $226.68 | $2,115.70 | 4% | $113.61 | $2,953.77 |
| 13% | $275.04 | $2,390.75 | 3% | $88.61 | $3,042.39 |
| 14% | $334.70 | $2,725.45 | 2% | $60.85 | $3,103.24 |
| 15% | $408.82 | $3,134.27 | 1% | $31.03 | $3,134.27 |
| Totals | $2,134.27 | $2,134.27 |
Well will you look at that… you end up with the same amount.
Well I guess I should have known that, addition and multiplication are commutative.
Here's what it looks like in graph form…
