Hacker Newsnew | past | comments | ask | show | jobs | submitlogin

It just so happens there is! (Sort of.) A one time sum can be compared with recurring annual sums by calculating the present value of each, taking into account prevailing interest rates. The present value of an infinite series of annual payments is given by the perpetuity formula: PV = (annual payment) / (interest rate). Assuming that the NSA budget won't grow, and using the 30-year treasury bond rate of 3.71%, the present value (or cost, really) of having an NSA forever is $270B. Of course, the NSA's budget is probably growing faster than 3.71% right now which ruins the math, since it would imply an infinite NPV. Also, to be totally accurate you would have to calculate the present value of the hyperloop which would be spent over some number of years.


What might you do with your infinite series to roughly estimate the NPV in your head without having to write anything down?

Especially when faced with certain tradeoffs, like comparing a $6B hyperloop with an agency with an annual budget of $10B?


Just divide the yearly cost by the rate of interest or inflation. $10 billion divided by 3.71% yields that $270 billion figure. Use whatever mental shortcuts work for arithmetic in other contexts. There's no need for an actual infinite series.

Explaining it the other way around, if you had $270 billion now, you could fund the NSA by $10 billion per year in perpetuity based on the interest. That's a simple calculation of $270B x 3.71%.


Must just be me. How about:

I'll trade 7 1/2 months of the NSA annual budget for one hyperloop.




Consider applying for YC's Fall 2026 batch! Applications are open till July 27.

Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact

Search: