Cumulative Inflation Impact on Unit Price

[SerenityNetworks]

I'm looking for a formula that gives me an average unit price value that considers annual inflation. For example:
Inflation is 2%
Year 1, Unit Price is 100.00
Year 2, Unit Price is 102.00 { =100*1.02 } for an average unit price of 101 { =(100+(100*1.02))/2 }.
Year 3, Unit Price is 104.04 { =102*1.02 } for an average unit price of 102.01 { =((100+(100*1.02))+(100*1.02*1.02))/3 }.
Year 4, Unit Price is 106.12 with the formula for the average growing to { =(100+(100*1.02)+(100*1.02*1.02)+(100*1.02*1.02*1.02))/4 }

I can keep expanding the formula. I only need to calculate it (this time) to get an average unit price for 5 years and 10 years. But I'm thinking there must be a formula more streamlined. I'm just at a loss as to how it might be constructed.

Any help would be greatly appreciated.

Thank you in advance,
Andrew

PS: Yes, I know I can shorten it using the power function, such as { =(100+(100*1.02)+(100*1.02^2)+(100*1.02^3)+(100*1.02^4))/5 } to get to year 5, but still it seems to me there is likely an easier way.

 

[Tetra201]

Excel has a special function for this, the SERIESSUM.

Your =(100+(100*1.02)+(100*1.02*1.02)+(100*1.02*1.02*1.02))/4 can be calculated as follows:

=100*SERIESSUM(1.02,0,1,{1,1,1,1})/4

 

[SerenityNetworks]

Fantastic! I figured there must be something as such.

Thank you!

 

[Tetra201]

You are welcome.