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Nice analogy! Although central banks implement rate cuts in order to spur economic activity (such as borrowing, spending, and investment), the effects take a while to catch on. This is why most central banks made more than a couple of successive rate cuts during the economic crisis. Of course they wanted to accelerate the activity in the economy so much that they slashed borrowing costs to record lows in order to pump up liquidity and stimulate the flow of cash.
After a series of rate cuts, however, the rate of return on a nation's investment also drops. This makes their assets relatively unattractive to investors so they'd rather put their money elsewhere, particularly in countries which offer higher rates of return. This gives rise to carry trade, where investors buy up the currency of the country with higher interest rates and sell the currency of the country with lower exchange rates. As a result, countries with higher interest rates (such as Australia) experience an appreciation of their local currency.
Your next statement states that the growth of an economy gives rise to an increase in price levels. This is why, when the country has convincingly moved out of the recessionary phase, central banks need to hike rates back up. Recall that slashing rates results to increased liquidity and, if the economy is already back on track, this could result to inflation. Raising borrowing costs would then mop up the excess liquidity in the market and bring inflation down, possibly to keep it within the central bank's target range (for instance, 2%).
