Geometric series vs. future value computation based on geometric series

In summary: You could also be using a cell reference to store the result in a variable.For example, you could use the following formula:=FV(28.83,10,0.05,0)
  • #1
IrinaK.
33
0

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

 

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  • #2
IrinaK. said:

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.
 
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  • #3
In addition to what Ray said, you could be formatting the cell with $28.83 in it to display two decimal places.
 

Related to Geometric series vs. future value computation based on geometric series

1. What is a geometric series?

A geometric series is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed number, known as the common ratio. The formula for a geometric series is a + ar + ar2 + ar3 + ... where a is the first term and r is the common ratio.

2. How is a geometric series different from a regular series?

A regular series follows a simple pattern, such as adding a fixed number to each term. A geometric series, on the other hand, follows a multiplicative pattern where each term is obtained by multiplying the previous term by a fixed number.

3. What is the future value computation based on a geometric series?

The future value computation based on a geometric series is a mathematical formula that calculates the total value of an investment or loan that grows at a constant rate over time. It takes into account the initial investment, interest rate, and number of periods.

4. How is the future value of a geometric series calculated?

The future value of a geometric series is calculated by using the formula FV = a * (rn - 1) / (r - 1) where FV is the future value, a is the initial investment, r is the common ratio, and n is the number of periods.

5. What are some real-life applications of geometric series and future value computation?

Geometric series and future value computation are commonly used in financial planning, investment analysis, and loan calculations. For example, they can be used to determine the growth of a retirement account, the total interest on a loan, or the value of an investment portfolio over time.

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