Single Year Returns from Geometric Average

Hello,

I am trying to write a script that will calculate possible calendar year returns from geometric cumulative returns.

The data I have are cumulative returns for year 1, 2 years, 3 years, 5 years, and 10 years. I would like to get the total returns for each of year 1-10. I understand that there are multiple possible returns to get there. I would prefer to find the mid point variables.

Year 1 is given, 2 and 3 are easily calculated, but once I get into years 4 and 5, I dont know how to write the code so that it returns 2 unknown variables at the midpoint.

I know I can do this in solver in excel but was hoping to do it in Matlab.

1 year: 2.1%
2 years: 2.2%
3 years: 2.3%
5 years: 2.4%
10 years: 2.5%

Any help would be great!

Thanks!