@ wrote... (4 months, 2 weeks ago)

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…

Category: business, Tags: accounting
Comments: 1
Comments
1.
Andrew @ February 25, 2020 wrote... (4 months, 2 weeks ago)

Neat, would not have guessed that! I can vouch for your math on this being right.

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