can the rate of interest become zero
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If you lent or borrowed for a year at a zero real interest rate, you would be exactly back where you started at the end of the year. I loan $100 to someone, I get back $104, but now what cost $100 before costs $104 now, so I'm no better off.
Typically nominal interest rates are positive, so people have some incentive to lend money. During a recession, however, central banks tend to lower nominal interest rates in order to spur investment in machinery, land, factories, and the like.
In this scenario, if they cut interest rates too quickly, they can start to approach the level of inflation, which will often arise when interest rates are cut since these cuts have a stimulative effect on the economy. A rush of money flowing into and out of a system could flood its gains and result in net losses for lenders when the market inevitably stabilizes.
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