Formula to calculate cost of increasing annual expense after a given number of years?

spazzybaz

New member
Joined
Mar 8, 2018
Messages
2
Hi folks!!

I have been trying to find a formula online to calculate the total cost of an annual expense that increases by a set % every year. I have had no luck after looking around for a few hours..

Example: I have an annual expense of $1000 that increases by 5% per annum. What formula can be used to calculate how much I have spent in total over 31 years without working out the amount for each individual year and adding them up.

I'm sure this is really quite simple but I have been unable to work it out for myself and cant find the formula online. Its driving me crazy!!!

Cheers!! :D
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,133
Hi folks!!

I have been trying to find a formula online to calculate the total cost of an annual expense that increases by a set % every year. I have had no luck after looking around for a few hours..

Example: I have an annual expense of $1000 that increases by 5% per annum. What formula can be used to calculate how much I have spent in total over 31 years without working out the amount for each individual year and adding them up.

I'm sure this is really quite simple but I have been unable to work it out for myself and cant find the formula online. Its driving me crazy!!!

Cheers!! :D
Do you know the formula for calculating compound interest?
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
3,014
Hi folks!!

I have been trying to find a formula online to calculate the total cost of an annual expense that increases by a set % every year. I have had no luck after looking around for a few hours..

Example: I have an annual expense of $1000 that increases by 5% per annum. What formula can be used to calculate how much I have spent in total over 31 years without working out the amount for each individual year and adding them up.

I'm sure this is really quite simple but I have been unable to work it out for myself and cant find the formula online. Its driving me crazy!!!

Cheers!! :D
This is an example of a (finite) geometric series; look up that formula and try applying it.

Or, it wouldn't be too hard to do it in a spreadsheet. Just make a column for the annual expense, and add those up in another column.
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,778
Hi folks!!

I have been trying to find a formula online to calculate the total cost of an annual expense that increases by a set % every year. I have had no luck after looking around for a few hours..

Example: I have an annual expense of $1000 that increases by 5% per annum. What formula can be used to calculate how much I have spent in total over 31 years without working out the amount for each individual year and adding them up.

I'm sure this is really quite simple but I have been unable to work it out for myself and cant find the formula online. Its driving me crazy!!!

Cheers!! :D
If you can write it out, you are on you way.

1000 + 1000*(1.05) + 1000*(1.05)^2 + ... + 1000*(1.05)^30

There is your Finite Geometric Series. Just add them up!
 

spazzybaz

New member
Joined
Mar 8, 2018
Messages
2
This is an example of a (finite) geometric series; look up that formula and try applying it.

Or, it wouldn't be too hard to do it in a spreadsheet. Just make a column for the annual expense, and add those up in another column.
Sweet!!! Thanks Dr!!!

So I had already been applying the compound interest formula but couldn't work out how to add them up.

The formula for a finite geometric sequence worked a treat..

Thanks everyone!! You're Legends!!!
:p
 
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