Questions: Rental costs for office space have been going up at 8.5% per year compounded annually for the past 7 years. If office space rent is now 29 per square foot per month, what were the rental rates 7 years ago? The rates 7 years ago were about per square foot. (Round to two decimal places as needed.)

Solution Steps

To find the rental rates 7 years ago, we need to reverse the effect of the annual compound increase. This can be done by using the formula for compound interest in reverse. We know the current rate and the annual increase rate, so we can calculate the original rate by dividing the current rate by the compound factor over 7 years.

We are given the current rental rate, the annual increase rate, and the number of years. Specifically:

• Current rental rate: \( \$29 \) per square foot
• Annual increase rate: \( 8.5\% \) or \( 0.085 \) as a decimal
• Number of years: \( 7 \)

To find the rental rate 7 years ago, we use the formula for compound interest in reverse: \[ \text{Original Rate} = \frac{\text{Current Rate}}{(1 + \text{Annual Increase Rate})^{\text{Years}}} \]

Substitute the given values into the formula: \[ \text{Original Rate} = \frac{29}{(1 + 0.085)^7} \]

Calculate the original rate: \[ \text{Original Rate} \approx \frac{29}{1.7474} \approx 16.3829 \]

Round the original rate to two decimal places: \[ \text{Original Rate} \approx 16.38 \]

Final Answer