If I have monthly rent at acquisition of $8,000 per month x 3% growth x 12 = $98,880 of GPR at the end of year 1. If I want to show this monthly & have each month compounding while still adding up to $98,880.
How would I do this formula?
All methods & insights would be appreciated.
rent * (1+growth)^((month-1)/12)
Doesn’t add up to 98,880
Annual to monthly —> (1+ Annual GR) ^(1/12)-1
Tried that already. Doesn’t add up to 98,880.
Call me crazy... none of these add up to 98,880
You’re right!
That’s why I’m confused… I knew those formulas before this post.
…still can’t figure it out
Unless I’m missing something.. you just divide 3% by 12, and then grow your GPR by that amount each month. Should be an easy formula for chat gpt to write for you.
So I think it doesn’t add up because rent isn’t suppose to grow monthly since they are annual leases.
If you use the =1.03^(1/12)-1
As the monthly growth rate.
It gets you to what the rent should be in the next year. Which if you multiply that by 12 gets you to the number.
Just had an interesting conversation with Chat GPT about this, as I was also stumped and not getting the numbers to match. Not sure if I should feel dumb or not, but at least I learned something. GPT also amazes every time I use it like this. The quick answer is that for your monthly version you cannot simply use 3%/12. The more accurate number is 0.2466%. Using that figure, you'll get it to match with your $98,880 amount.
Here's GPT's explanation of why that is:
To accurately break down an annual interest rate into a monthly rate that, when compounded, results in the equivalent of the annual rate, you cannot simply divide the annual rate by the number of periods (months, in this case). Instead, the process involves understanding that each month's interest will be calculated on the total amount from the previous month, including prior interest added.
Why 0.2466%?
The more accurate monthly rate considers the compound interest formula, which is essential for converting annual rates to monthly when the interest compounds:
For an annual growth rate of 3%, or 0.03 when expressed as a decimal, the math works out as follows:
This calculation accurately distributes the effect of annual compounding into monthly increments. If you were to use 0.25% instead, you're effectively applying a slightly higher monthly rate, which compounds to more than a 3% annual growth rate after a year due to the exponential nature of compound interest.
Practical Implication
Conclusion
Why is 0.246 Measures of training-program effectiveness encompass several dimensions:6% more accurate than 0.25% for your problem? Because it precisely accounts for the compounding effect over twelve months, ensuring that the growth rate you apply each month accurately results in a 3% annual growth when compounded, matching the principles of compound interest. This accuracy is crucial for financial planning, investment analysis, and any scenario where the subtleties of growth over time have a significant impact.
Correct you want to use 0.25%.
Because you can’t do 3%/12 like you said.
You can arrive to this 0.25% by:
=1.03^(1/12)-1
However, it still doesn’t add up to $98,880.
This is because the way the rents are leased (yearly). They do not compound monthly so you can compound to arrive at the rents you should charge at the beginning of the following year. Can’t sum them up to equal $98,880.
I think you misread my comment. You cannot use 0.25% - that is where your error is. Plug in 0.2466% and you'll arrive at $98,880. I just did it in excel and it worked.
Also, don't you work in multifamily? You keep saying leases are yearly, which yes is true on average. However, your post was asking about GPR. GPR can of course compound monthly at a 3% annualized rate.
I’m getting $97,553. When I do it.
Where do you think I’m going wrong?
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