I'm not sure if this is the right place to ask this kind of a question, but here it goes.
I have the following information:
- A = Total amount needed
- B = Number of periods (monthly, 12 payments of equal value then increased by the percentage increase repeated for B number of periods or annually (once per year) increasing by percentage increase every time for B number of periods)
- C = Percentage Increase (whether increasing every payment or every 12th payment)
I'm tasked with finding:
- The starting amount payment value (X) to equal the total amount needed (A) if paid out for (B) periods, and increasing by (C) percent
I know I can find the starting value in today's dollars or the end value according to
A * ((1 + C/100) ^ B) = X or A = X / ((1 + C/100) ^ B)
I also know you can quickly calculate something like compound interest with this equation:
A * ((1 + C/100) ^ (B / 12)) = X
for 12 variable, compounding payments in a period split to equal (C) rate of return.
What is the proper equation to find the starting payment amount (then increasing by (C) percent every period) for my inquiry? I'm looking for two conditions, the starting payment value whilst receiving 12 payments of equal value and then increasing by (C) percent for the next 12 payments (yearly) or receiving one payment per year, each increasing by (C) percent over the previous payment.
Excuse my ignorance if this is a duplicate question, but I'm having a hard time finding an applicable answer on this site given my lack of terminology.
I'm looking around and I came across this site: http://www.hughchou.org/calc/formula_deriv.php
The page above is about paying off a mortgage, which isn't quite what I'm looking for. The value I'm trying to find is static, not an increasing loan amount. It's just receiving increasing payments to meet that defined specific value. I think that would be on the right track, but omitting the increase in principal.