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If my school district says it wants to extend an existing bond and not increase the tax rate and the assessed value of my home never increases/decreases(hypothetical), will my taxes stay the same?

If the assessed home value increases, is the school district paying down the bond faster? Or only taking a fixed amount according to a repayment schedule?

If my school district says it wants to extend an existing bond and not increase the tax rate and the assessed value of my home never increases/decreases(hypothetical), will my taxes stay the same?

If you refinance your mortgage, does your mortgage payment have to go up? No.

Refinancing a bond works the same way.

If the assessed home value increases,

Your home value might increase while others decrease. If the county-wide valuation increases, the school board will get more money.

is the school district paying down the bond faster?

Is there a property tax "slice" dedicated to that bond? If so, they might pay it off faster, or they might accumulate the extra money in a rainy day fund in case property tax receipts drop in the future.

You'll have to ask them.

Or only taking a fixed amount according to a repayment schedule?

In my county, each dedicated bit of the property tax pie is a a percentage. When property taxes go up, the pie gets bigger.

YMMV but I doubt it. In any case, your county should have a web site explaining all this.

If the assessed home value increases, is the school district paying down the bond faster?

Bonds are different than loans. With bonds, you don't generally have the option to "pay them down faster" (unlike, say, a loan or line of credit). The investors that buy the bonds expect regular, consistent payments and don't like it when they get paid off early (that means they get less interest going forward). Bonds can be callable, meaning the issuer may have the option to "buy back" the bond, which essentially is paying off the entire debt plus some compensation for the early repayment, but they can't just make extra payments and retire the debt early.

Bonds and tax rates are separate issues, although sometimes they will be combined into a single bill/initiative; that is, sometimes a bill will be proposed along with a tax to pay for it. But a bond, by itself, doesn't affect tax rates; unless there's an additional tax specifically authorized, the district simply has to find money in their existing funds to pay the interest.

Conversely, taxes don't generally affect bond repayment. Paying off a bond isn't like paying off a credit card, where you can send in as much money as you want and have it taken off the principal. Unless there are specific provisions in the bond, the issuer has to keep paying interest on the original amount. Sometimes, however, the issuer of a bond will find themselves with more money than they were expecting, and will buy back the bonds. Unless the bond has provisions forcing the holder of the bond to let the issuer buy the bond back, the issuer has to offer enough money to get the holder of the bonds to voluntarily sell. If interest rates have fallen, then the issuer will probably have to pay more for the bond than they received when they issued it. Another way that additional funds can decrease outstanding bonds is if the issuer has rolling bond issues. This is where instead of selling one long-term bond, the issuer will sell several short term bonds one after another, each one funding the redemption of the previous. Doing this allows the issuer to simply not issue the next bond, if their funds have increased to the point that they can afford to pay off the previous bond without issuing another.