A central bank issues currency and wants to target the price of apples in terms of that currency. So it opens an apple window, and posts a sign promising to buy or sell unlimited quantities of apples at $1 each. Done. Arbitrage ensures that the market price of apples in the economy is always $1 each, plus or minus transportation costs to or from the central bank's apple window.
If the central bank wanted to target 2% apple price inflation, it could simply change the price on the sign daily, so it rises at 2% per year.
Suppose the central bank found it was selling too many apples, and it was scared of running out of apples reserves? It could sell something else it owned (maybe government bonds?) to reduce the stock of currency in circulation, to reduce the quantity of apples it needs to sell.
Suppose the central bank found it was buying too many apples, and was scared it was running out of room to store all its apple reserves? It could buy something else (maybe government bonds?) to increase the stock of currency in circulation, to reduce the quantity of apples it needs to buy.
(That's how the gold standard worked, except it was gold rather than apples.)
If the central bank bought or sold exactly the right amount of that something else, and did so quickly enough whenever it saw people running to the apple window carrying either currency or apples, it would never need to buy or sell any apples. The apple window could remain open, but would never have any customers.
Or it could close the apple window, and just watch the market price of apples instead of watching whether the people running to the apple window were carrying currency or apples.
(That's how inflation targeting works, except it is a basket of apples, bananas, and haircuts, and other stuff, rather than just apples.)
But maybe buying and selling something else (like government bonds?) isn't the only way the central bank could reduce the amount of buying and selling it does at the apple window. Maybe an alternative is varying the rate of interest it pays people to hold currency?
The idea is simple. If the central bank sees people running towards the apple window carrying currency, wanting to buy apples, it raises the rate of interest it pays them to hold currency until they stop wanting to buy apples from the central bank. And if the central bank sees people running towards the apple window carrying apples, wanting to buy currency, it lowers the rate of interest it pays them to hold currency until they stop wanting to buy currency from the central bank. The idea is that the central bank adjusts the rate of interest it pays on currency to vary the demand for currency, as an alternative to varying the supply of currency by buying or selling something else (like government bonds).
And paying interest on currency is a lot easier administratively if the central bank money that people hold is not in fact paper currency but electronic "currency" in chequing accounts at the central bank.
(Which is how interest on reserves is supposed to work, except that the central bank farms out the management of those chequing accounts to commercial banks, and those commercial banks are the ones who have chequing accounts at the central bank.)
Would it work? Well that depends.
If the interest on currency is paid by printing more currency, then it won't work. Because increasing the rate of interest on currency from 0% to 1% means increasing the growth rate of the supply of currency from 0% to 1%. It's like a corporation trying to increase demand for its shares to raise their price by announcing a future 101 for 100 stock split, except in this case we are talking about a corporation that lets its customers do their own stock splits any time they like, if they prefer the convenience of two $10 notes to one $20 note or vice versa. The equilibrium value of the currency is unchanged at the time that the higher interest rate is announced, but that equilibrium value will now be falling at 1% per year relative to what would have happened otherwise.
Indexing the interest rate on currency to inflation would be even worse, if that interest is financed by printing more currency. It is like a corporation that promises a 2 for 1 stock split if the market price of its shares falls by 50%. The only effect is that the market price of a share falls by 75% instead of 50%. Yes, the only equilibrium (if it exists) is if the value of the currency stays exactly the same (update: other things equal); but that equilibrium is horribly unstable. Because the further inflation rises above target the more the central bank increases the growth rate of the currency supply. And the further inflation falls below target the more the central bank reduces the growth rate of the currency supply.
[Yes, I am having flashbacks to the Neo-Fisherian "sign wars" kerfuffle.]
If the central bank wants to increase the demand for currency by raising the interest rate it pays on currency it must ensure that the interest is financed by selling something else, and not by printing more currency. This ensures that raising the interest rate has no effect on the growth rate of the supply of currency, and so will only affect the demand for currency, by increasing it.
Or it could pay interest on currency in the form of apples, which really would be a "real" interest rate. Which would mean that currency is a consul (perpetuity) paying an annual (or daily) apple dividend, which gives it a determinate real value much like an infinitely-lived apple tree. And by varying the apple dividend rate the central bank could ensure that the market value of an apple tree stays equal to a fixed number of apples (or a number of apples that declines at 2% per year).
But then it might as well just reopen the apple window, if it doesn't find it a hassle to handle apples (or baskets of apples, bananas, and haircuts, and other stuff).