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Performance of an investment when contribution values are variable

Personal Finance & Money Asked on May 17, 2021

Every two weeks in 2020 (thus, 26 times), I’ve contributed some money (usually about $200, but sometimes more or less) to a bond fund. The starting value was $21000 and the current value is $28500. I’m trying to determine the annualized performance of this "annuity".

Because the contributions were so variable, I decided that the proper course was to calculate 26 future values using the formula (1+ r/26)p, where r is the annualized performance, and p is the number of periods left in the year, and then sum them up.

Thus, add $21000 to the results of these 26 formulas to get $28000.

But the problem is that the only value for r which makes the series work is 33%, and that can’t be right (if for no other reason than this is a Total Bond Index fund).

What am I doing wrong?

Periods
Until EOY       Formula
26          $164 * (1+.33/26)^26 = $ 227
25          $201 * (1+.33/26)^25 = $ 276
24          $986 * (1+.33/26)^24 = $1344
23          $201 * (1+.33/26)^24 = $ 272
...
 4          $101 * (1+.33/26)^4  = $ 106
 3          $201 * (1+.33/26)^3  = $ 209
 2          $201 * (1+.33/26)^2  = $ 206
 1          $201 * (1+.33/26)^1  = $ 204
                                   -----
                               Sum $7416

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