I only use one account for sinking funds, personally. I use Excel to track the money I put into it, so every penny is allocated to this or that sinking fund.
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I do also have nonfixed sinking funds. Car repair, yes, also a fund to save up for a new car in the (knock on wood) distant future when this one dies, home repair (and yes, I have the amount for a roof in mind, but I haven't saved anywhere NEAR enough for it yet, but that's also a distant item). We don't take vacations per se, but my annual visit to my mother is in there.
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Even though it's one account, I don't "just" pay for whatever it is out of the account. If I have a car repair that's $400 and I only had $350 at the time, then I'd take $350 out of the account and cover the rest under my regular monthly cash flow. You can do whatever you want, but I prefer to do it this way because that's how I can track how much I have for every single fund. Some funds I won't touch until I have enough (saving up for some paint and stuff for the bathroom, for example) and if I just dump it all into an account and don't track what I have for what, then I would never know if I had enough for anything. Even stuff that is not elective, like a car repair, I feel better knowing "hey, we covered 100% of that one" or "we caught all but $50, not bad" than just taking it out of the account and not having a clue whether the car repair meant that we would not have enough when the life insurance came due, or the car excise tax, etc.
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We don't have a sinking account AND a home repair account AND a vacation account - those are the sinking accounts.
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Some people have a bank account for every sinking fund, and that's very legit. I don't because I have 17 sinking fund categories and I just think it's a waste to spend all that time transferring in and out of that many accounts when I can just record it all on a spreadsheet and be done with it.
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If you would rather just have an account and not track it and just use it to withdraw from whenever a qualifying event comes up, that already puts you ahead of many people. Whatever works, right?
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We used to call our stuff short term and long term savings too. But now we changed to sinking funds and emergency fund.
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Sinking funds are any predictable expenses. They include things we know for a fact we will spend (life insurance premium, for example), plus some things we can predict we'll probably use sooner or later even if we hope we don't (car repair, medical deductible). It even includes a couple things we just plain want (saving up to paint the bathroom and put some new towel bars and stuff in). In any event, we expect to spend them at some point or another, and I've worked hard to make sure I have planned to catch pretty much any contingency (the funds are not nearly funded enough but I'm working on it). This is money meant to be spent, and I don't feel bad about withdrawing from it.
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The emergency fund is the last ditch thing that covers only emergencies. Since I can predict our car may need repair at some point, I don't consider it an emergency, so I have a sinking fund for that. The goal is to not touch this fund, but it's there if we need it. Job loss would be one reason to touch it. Or other scenarios I can't think of or don't want to. This is "in case of emergency, break glass" kind of money. 3-6 months living expenses is the recommendation. I've built it up to 2 weeks, sigh, but I'm working on it.