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.