Rental costs for office space have been going up at 

7.97.9​% 

per year compounded annually for the past 

44 

years. If office space rent is now 

​$2424 

per square foot per​ month, what were the rental rates 

44 

years​ ago?

Question content area bottom

Part 1

The rates 

44 

years ago were about 

​$enter your response here 

per square foot.

​(Round to two decimal places as​ needed.)

To determine what the rental rate was 44 years ago, we can use the formula for compound interest, which is:

\[
A = P(1 + r)^t
\]

Where:
- $ A $ is the current amount (rent per square foot now) = $24.24
- $ P $ is the original amount (rent per square foot 44 years ago)
- $ r $ is the annual growth rate = 7.979% or 0.07979
- $ t $ is the number of years = 44

We want to solve for $ P $, the rent 44 years ago:

\[
P = \frac{A}{(1 + r)^t}
\]

Substituting the known values:

\[
P = \frac{24.24}{(1 + 0.07979)^{44}}
\]

Now, I'll calculate this value.The rental rates 44 years ago were approximately **$0.83** per square foot per month.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:
1. How would the formula change if the growth rate were compounded monthly instead of annually?
2. What would the rental rates be in 10 years, assuming the same annual growth rate?
3. How does the length of time (e.g., 20 years) affect the final rent when compounded at this rate?
4. How would a decrease in the growth rate to 5% affect the rent 44 years ago?
5. What is the difference between simple interest and compound interest in terms of rental growth?

**Tip:** In compound interest calculations, the frequency of compounding (monthly, annually, etc.) plays a significant role in the final amount.

Rental costs for office space have been going up at 7.979% per year compounded annually for the past 44 years. If office space rent is now $24.24 per square foot per month, what were the rental rates 44 years ago?

Find out how to calculate the office rental rates from 44 years ago, using the compound interest formula. Given a current rent of $24.24 per square foot and an annual growth rate of 7.979% over 44 years, discover how historical rates are determined. This problem explores exponential growth concepts and compound interest formulas. Suitable for Grades 10-12.

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