In order to determine the value of the rent after x years, we need to generate a function which would relate the value of the rent and the time in years. The rate by which the rent increases is said to be 3.5% per year. So, if we do it manually, we would have:
value of the rent = 225000 + 225000 (.035) + 225000 (.035)(.035) + ........
However, this is a tedious and long process since we need to continue until year 8. We need to simplify it to an expression. We do as follows:
value of the rent = 225000 + 225000 (.035) + 225000 (.035)(.035) + ........
We factor out the initial rent,
value of the rent = 225000 (1 + (.035) + (.035)(.035) + ........)
Then, we simplify the terms inside the first parentheses,
value of the rent = 225000 (1 + (.035))^x
where x is the number of years. We then substitute 8 to x to determine the value of the rent.
value of the rent = 225000 (1 + (.035))^8 = 296282.03
