This is a hard question and software people will typically not want to be pinned-down on specifics without consulting with you extensively, because the depth of requirements for software projects vary dramatically. You’re asking for very little functionality (which is great!) but the bulk of costs of software construction are not in the core functionality, they are in polish, bug-fixing and edge-case handling, which you included in your requirements (“simple, secure, and easy to use”) but would need to be a lot more specific about, in order to get a result you’d be happy with. It’s really hard to give these kinds of estimates without those conversations.
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To just satisfy the requirements, I could imagine doing the non-payment-processing version very cheaply using Typeform or another “survey builder” for the UI, and a simple backend that just pulls the results out of Typeform and sends notifications. I could imagine throwing a prototype for this together in a few days of time for someone like me (so less than a few thousand $) but it would probably not work well, be reliable, etc. at that level of polish. Also, few freelance developers of quality will take on a project like this at that price point, because they have “seen it all before” and know that the edge cases and polish are likely going to result in a 10x cost inflation at a minimum.
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Payment processing increases the cost a bunch because it adds new requirements for security, ease of understanding & debuggability, etc. You can often outsource the actual UI for it to e.g. Stripe Checkout though so it may not make a huge impact.
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I don’t think you’ve given enough information to answer “what would be the best way to go about it?” For example it sounds like you need software help, but you might also need graphic design help, product design/UX help, etc. For software help I know that freelance developers will bid on your projects on various sites (I’m not familiar with which sites are currently considered reputable and I haven’t done this myself so I don’t know how hard it is to figure out which bidders are any good). But it’s unlikely you’ll produce a “simple, secure and easy to use” product without getting help in other domains as well. It is sometimes possible to convince people to work with you for free if they like your idea (and you).
Great analysis!
I would strengthen the term+self-fund recommendation for readers of LW. You say it only makes sense if you “expect to be very wealthy”; however, it seems to me that it is pretty easy, over the course of 20 years or so, to plan to save up a few hundred thousand $ to self-fund after that point. If that doesn’t sound easy then it is not so clear that cryonics is for you; and IUL isn’t solving the problem because you still have to pay the money in expectation. It seems like IUL only makes sense if the term insurance gets expensive before you can conceive of a way to save the money on your own. I guess it also makes sense if you aren’t conscientious about saving or making term payments. But it seems to me like you pay a lot for this convenience.