Neco 2022 Government Question 30

A local government council receives three sources of revenue in year\,1: property rates \(\text{₦}80\) million, a federal allocation \(\text{₦}50\) million, and locally generated fees \(\text{₦}30\) million. The council aims to increase its total revenue by \(25\%\) over the next three years. To achieve this, it plans to raise property rates by \(10\%\) each year, keep the federal allocation constant, and grow locally generated fees by a constant annual percentage \(r\). Assuming the increases are compounded annually, determine the value of \(r\) (to two decimal places) required for the total revenue in year\,3 to meet the \(25\%\) target. Additionally, if the council must allocate \(40\%\) of its total revenue each year to infrastructure, calculate the infrastructure budget for year\,3.