Below is a useful flow chart for anyone studying monetary policy. Both the NCEA Level 3 and CIE A2 courses cover this topic.
Negative – lower interest rates might depress spending by some retirees who rely on interest income. But these counterproductive channels are small compared to the
Positive – lower interest rates = a lower propensity to save and a higher propensity to spend.

The side effects of monetary policy.
Falling interest rates = accelerating house prices = social problems and political anxiety.
If RBNZ kept interest rates at around 8% as in the 2000s to prevent the house price = New Zealand in deflationary spiral.
The economic and social consequences of deflation would be far worse than the (undeniable) problems with rising house prices. The low inflation / falling interest rate dynamic of the past two decades has been a global phenomenon, ultimately caused by a global change in the balance between savings and investment. The Reserve Bank of New Zealand could not have prevented this global trend from affecting New Zealand interest rates without causing severe damage to the economy. In New Zealand, the most important transmission channels are asset prices and the exchange rate. Falling interest rates tend to push asset prices up, which stimulates consumer spending. Falling interest rates also tend to reduce the exchange rate, which generates inflation via the prices of internationally-traded goods and services.
Source: Westpac Bank
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