@ wrote... (1 year, 6 months 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
@ February 25, 2020 wrote... (1 year, 6 months ago)

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

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