Total Rent Expense Calculation for a 7-Year Lease
What is the total rent expense for a 7-year lease with an initial annual rent of $85,000 and a 6% annual increase?
Final Answer:
The total rent expense for the 7-year lease with an initial annual rent of $85,000 and 6% annual increase is approximately $711,736.
Calculating the total rent expense for a 7-year lease involves determining the annual rent for each year and summing them up based on the given information. In this case, the lease starts with an initial annual rent of $85,000 and will increase by 6% each subsequent year.
To find the total rent expense, we need to calculate the annual rent for each of the 7 years of the lease. The annual rent follows a geometric sequence with the initial term as $85,000 and a common ratio of 1.06 (due to the 6% annual increase).
Here's how we can calculate the annual rent for each year:
Year 1: $85,000
Year 2: $85,000 * 1.06 = $90,100
Year 3: $85,000 * 1.06^2 = $95,416
Year 4: $85,000 * 1.06^3 = $101,047
Year 5: $85,000 * 1.06^4 = $106,999
Year 6: $85,000 * 1.06^5 = $113,279
Year 7: $85,000 * 1.06^6 = $119,895
By adding up the annual rents for all 7 years, we get the total rent expense:
Total Rent Expense = $85,000 + $90,100 + $95,416 + $101,047 + $106,999 + $113,279 + $119,895 ≈ $711,736
Therefore, the total rent expense for the 7-year lease with an initial annual rent of $85,000 and a 6% annual increase is approximately $711,736.