Geometric series vs. future value computation based on geometric series

[IrinaK.]

Homework Statement

Hello!

Revising geometric series, I have understood that I have the following issue - I have read again about these series and, please, take a look at what I have gotten as a result (picture attached).

If I calculate a future cash flow, that is I take, for example, a = 0,5 (it can be 100, 5 or any other number), r = 0.5 (also can be any other number), n = 10 (same), I get completely different results if I use the sum of geometric series and the future value calculation. Why? In all these cases I compute the sum of a multiplied by r within an n period.

I would be grateful for your help - I obviously miss some basic understanding.

PS: I have tried to paste a picture within this text, the program did not allow that; so I have to upload it.

Homework Equations

The Attempt at a Solution

 

[Ray Vickson]

Homework Statement

Hello!

Revising geometric series, I have understood that I have the following issue - I have read again about these series and, please, take a look at what I have gotten as a result (picture attached).

If I calculate a future cash flow, that is I take, for example, a = 0,5 (it can be 100, 5 or any other number), r = 0.5 (also can be any other number), n = 10 (same), I get completely different results if I use the sum of geometric series and the future value calculation. Why? In all these cases I compute the sum of a multiplied by r within an n period.

I would be grateful for your help - I obviously miss some basic understanding.

PS: I have tried to paste a picture within this text, the program did not allow that; so I have to upload it.

Homework Equations

The Attempt at a Solution

I normally do not respond to postings containing screen shots (as they are often unreadable), but I will make an exception for you this one and only time. I suspect that the function FV(rate,nper,pmt,(pv) ) is a built-in EXCEL function, that may round off to the nearest cent. (I don't know for sure, having not checked it myself). Your "manual" calculation reports the results to higher precision.

 

[Mark44]

In addition to what Ray said, you could be formatting the cell with $28.83 in it to display two decimal places.