Why does a rise in interest rates lead to a fall in inflation?

A rise in interest rates increases the cost of borrowing and increases the reward for saving. This means that there is a double effect, people are disincentivised to borrow money and spend it, as well as having additional incentives to save their money rather than spending it and putting it into the money cycle. This means that there are withdrawals from the circular flow of income, decreasing the overall amount of money in the economy. A fall in the amount of money in the economy means that there is a fall in the demand for products, decreasing the upward pressure on prices, creating a fall in inflation rates.