Math Is Fun Forum

mukund_am@yahoo.com

Member

Registered: 2017-04-10

Posts: 1

Sum of cost over N yrs of item costing X this year with N% inflation

My problem - cost of an item for this year is 100 (say X). Cost increases every year by 8% (say Y%) due to inflation. I would like to know the summation of cost of item for 3 years (say N year).
i.e. Year 1 cost - 100, Year 2 cost - 108, Year 3 cost - 116.64, summation of cost of item for 3 years = 100 + 108 + 116.64 = 324.64

I would like the formula where X, Y and N mentioned above are parameterised?

Regards,
Mukund

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Sum of cost over N yrs of item costing X this year with N% inflation

hi Mukund

Welcome to the forum.

Yes, there is a formula for this.

A sequence that increases by a factor r is called a geometric progress (series).

The formula is

where Po is the initial amount (=X), Pn  is the amount after n years and r (= 1+Y/100) is the growth rate.  If the interest rate is 8% then the amount grows to original + (0.08 x original) = original x 1.08 and that's what you use for r.

As r is greater than 1 you can reverse the formula to avoid negative bits:

Look here: http://www.mathsisfun.com/algebra/seque … etric.html

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sum of cost over N yrs of item costing X this year with N% inflation

Hi;

Since you just asked for a formula...

this is easy to derive from the recurrence relation and the summation of it, although I would not want to do it by hand. I see that bob bundy already explained one method to you...

The last part of your question... parameterized with respect to what?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Sum of cost over N yrs of item costing X this year with N% inflation

hi bobbym,

The two formulas are the same; just different symbols.  You have used the poster's; I have used MIF's.  The 'proof' of the formula is 3/4 down that page.  Or you may wish to post a 'help me' and I'll show you

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sum of cost over N yrs of item costing X this year with N% inflation

Hi bob bundy;

I did not mean I thought your solution was incorrect, I figured it was a rearrangement of mine..

It was the last part of the OP's question that might need to be done. Usually, when I see something parameterized it is in terms of one variable. Sort of like

Y = f(N)

X =g(N)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Sum of cost over N yrs of item costing X this year with N% inflation

hi bobbym,

I was only joking about trying to teach you anything, anyway.  That would be a red letter day!

I think we may have done all he wants.  He may just be using the word parameter, where we would use variable.  Let's wait and see.

Y in your formula needs to be a decimal not a percentage.  eg. Y = 0.08 not 8%

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sum of cost over N yrs of item costing X this year with N% inflation

Hi;

Not true, I have learned a lot from your stuff.

The Y is already set up for numbers like .08

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.