How does the interest rate affect government expenditure and government revenue?

An increase in the interest rates will put the government into more debt due to an increase in the interest amount on borrowings. This will lead to higher government expenditure. At the same time, the higher interest rate will force people to borrow less money leading to a fall in investments which will reduce the demand in the economy thereby reducing inflation in the economy. A fall in inflation will put people into lower income tax brackets thereby reducing the revenue of the government. So, in this way, the interest rate affects government revenue and government expenditure.