Formula for calculating cumulative cost when price increases each year?

Question

Say I'm a homeowner, and my energy bill is $1500/year. However, every year, the price increases by about 4%.

It's fairly trivial to figure out what my bill will be in year 5 or year 10, but what formula do I use to calculate the total amount I paid from year 1 through year 10?

There must be a more elegant way than:

$1500 + ($1500 * 1.04) + (($1500 * 1.04) * 1.04) + ...

and iterating that 10 times.

I've searched extensively for a formula that calculates this, and come up empty handed. Help!

Answer 1

You have a geometric series, which can be summed. Your series is $1500(1+1.04 + 1.04^2+\ldots + 1.04^{n-1})$ for $n$ years.The sum is $1500\frac {1.04^n-1}{1.04-1}$