Hey SteveCHOCC.
Are you familiar with annuity and loan repayment models using the framework of difference equations?
Hello, I'd be very grateful for help to identify a GENERAL equation or formula for our condominium reserve analysis: We have estimated the amount of $ needed in each of the next 50 years to pay for "capital replacements", like new roofs, etc. The projected needed $ amounts for some future years is low, but for some other future years is very high, for example, $45,000 five years from now, then down to $25,000 three years after that, then back up to $50,000 seven years after that ... up and down by very different amounts at various points-in-time that are NOT evenly spaced, e.g., yearly intervals of 3, 5, 7, 3, 5, 2, 7, 3, etc.
What is a GENERAL formula to determine the amount of $ that must be saved in each of the next 50 years in order to ensure that enough $ will be on-hand at each future year when a pre-determined estimated $ amount will be needed?
I'm thinking there could be TWO different formulas:
One that keeps the annual required $ saved amount CONSTANT throughout the entire 50-year period,
and a different formula that allows the annual required $ amount to be saved to be changed (up OR down) at desired future years, for example: if we wanted the required annual $ amount being saved to be increased by 5% in each successive year rather than keeping it constant, OR alternatively, if we wanted to SKIP saving any amount in certain years, etc.
Thank you very much for any help !! SteveCHOCC
chiro, thanks for your reply. I'm very familiar with loan amortization and annuity tables, and there underlying formulas. However, I don't know what you're referring to when you say "using the framework of difference equations". If it's not asking too much, could you please describe, conceptually, what "difference equations" are, and/or perhaps provide a simple example? Referring back to my original post, if I had the simple situation of needing to calculate the "constant" annual $ amount necessary to save, which together with a stated % rate of interest earnings on the saved dollars, that would accumulate to just ONE predetermined needed $ amount at ONE predetermined future year, then I'm familiar with using the annuity-type formula to calculate what that "constant" annual saving $ amount would need to be. But I don't know how to perform that type of calculation for a situation in which there are MANY different years in the future which each have a DIFFERENT $ amount accumulated by that time. In my scenario in which I'm projecting 50 years into the future, during which there could potentially be 25 DIFERENT fairly large $ amounts needed in 25 of those 50 years, I realize I could create 25 separate formulas, one for EACH of those 25 years that has a projected cash need, but I was wondering if there is a more concise way of calculating the necessary amount of annual $ saving, in order to not have to have 25 separate formula calculations. Is there a way to structure just ONE formula, even if it's complicated (or even a few separate formulas) that can do the necessary calculation even if there are 25 different future years that have a cash need, or is it, indeed, necessary to have a separate calculation for EACH future year?