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

#### spazzybaz

##### New member
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!! #### Subhotosh Khan ##### Super Moderator Staff member 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!! Do you know the formula for calculating compound interest?

#### Dr.Peterson

##### Elite Member
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!! 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 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!! 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
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!!! 