Subscription Costs

Exponential growth is when something increases at a rate proportional to its current size. The larger the number, the larger the rate—the larger_er 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 :