Q$1.$ A small shopping complex can be constructed for $$50,00,000.$ The financing required $5,00,000$ down $($you pay$)$ and a $45,00,000$ loan at $10\%$ with equal annual payments. The gross income for the first year is estimated at $6,00,000$ and is expected to increase $5\%$ per year thereafter. The operating and maintenance costs and taxes should average about $40\%$ of the gross income and rise at the same $5\%$ annual rate. The resale value in $30$ years is estimated at $1,00,00,000.$ Find the rate of return on this investment over the $30-$year life. Solve the problem assuming that the increase follows $($i$)$ arithmetic gradient and $($ii$)$ geometric gradient.