Exponential growth is when something increases at a rate proportional to its current size. The larger the number, the larger the rate—the largerer the number. This describes how inflation impacts the average periodic increases of subscription prices.

Determine the total projected lifetime cost of a subscription service assuming:

  • - starting payment
  • - annual inflation
  • - number of payments per year at the same price (e.g. 12 for monthly or 1 for annually)
  • Natural exponential growth as a simplification of market factors and month/year-end effects.

Example

  • Starting monthly price: $19.99
  • Estimated average annual inflation: 3%
  • Time: 30 years

Program in Farad

Method

Future value of an initial price after elapsed time with inflation rate :

Integrate over time to add up all of the payments:

Evaluate from to :

Simplify:

Multiply by number of payments per year :