Interest rates are the main determinant of investment on a macroeconomic scale. Broadly speaking, if interest rates increase across the board, then investment decreases, causing a fall in national income. Note that if interest rates are high, that means the broad economy is doing well and thus people will be willing to borrow money at higher interest rates.
Interest rates are set by a government institution, usually a central bank, as the main tool of monetary policy. The institution offers to buy or sell money at the desired rate and, because of their immense size, they are able to effectively set i*n.
By altering i*n, the government institution is able to affect the interest rates faced by everyone who wants to borrow money for economic investment. Investment can change rapidly to changes in interest rates, affecting national income.
Through Okun's Law changes in output affect unemployment.