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The reason for this is that the interest rate is, essentially, the price of money. As you know from basic economics, the price of a good or service is determined by the supply of and demand for that thing. Money is no different.
This means that when the supply of money changes, the price of money will change too (if demand does not change). When the supply of something goes up, its price goes down. When supply goes down price goes up.
The reason behind that is that if there is more money available, lenders cannot charge as much because there is more competition to lend.
We can think of interest rates as the price paid for borrowing money. Thus interest rates also are influenced by the laws of demand and supply. When the money supply increases it means that more money is available in the economy for borrowing and this increased supply, in line with the law of demand tends to reduce the interest rates, or the price for borrowing money down. Similarly when the money supply decreases, it will tend to push up the interest rates.
Of course, supp;u of money is one of the two factors that determine the interest rates. The other factor is the demand for money. This means the demand for borrowing money for investing in business or for consumer purchase on credit. The interest rates tend to increase when demand increases and decrease when demand increases.
The equilibrium rate of interest is the rate at which the demand for money equals the supply of money.
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