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A sinking fund and emergency fund are two completely different things. An emergency fund are for unexpected things. Unexpected medical procedure, hot water heater blows after 2 years, transmission fails on your car just outside of the original warranty, those are emergencies. A sinking fund is where you plan on using your car for 7 years and you know a replacement will cost $30,000 so you pay yourself $30k into an account over 7 years each month, then at the end of 7 years you have $30k. That's a sinking fund. You don't touch that money unless it is going towards the end target.
As for a budget it is applicable for in everyone's situation. A budget allows you to "pay yourself first". In a budget the essential things that need to be taken care of are are a roof over your head, food on the table, keeping the lights on and the heat pumping, and getting to and from work. After that how you choose to spend your money is up to you. Whether you start by paying yourself the 20% or you spend it on whatever else, that is up to you. The budget allows you to see where you are spending your money and make your money behave.
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