## Rent Stability

As usual, I wasn’t thrilled when my landlord told me about this year’s rent increase. As someone familiar with how exponential growth works, I understand the power of the small, consistent percent increase.

After some mild protests, the landlord came back with some good news: he was going to reduce my increase by $25 per month! I wasn’t exactly thrilled with that, either, but it’s a gesture. And I thought to myself “At least I won’t be paying future increases on that $25!”

Which got me thinking: if my rent goes up 3% every year, how much of a difference will that $25 make? The answer: not much. In my lifetime, anyway.

At 3% per year, the $25 difference in rent now will be a $30 difference in 5 years. In 15 years, the difference in the two rents will be around $40. And if I stick around for 50 years, the difference will be about $90.

If I could stay here for 200 years, I’d see a big difference: almost $10,000! But then again, my rent would be around $1 million per month.

I’ll have to be content knowing that, while in the short term I don’t see much benefit, I win out as *t* goes to infinity.

*Click here to see more in Application.*

Maybe I see a math problem for students. What is your rent now based on given info?

It’s a good question, one that I was actually wondering myself initially. It’s also interesting (and perhaps surprising) that some of the given information tells you

nothingabout the current rent.I think you’re measuring the wrong thing! You’ll save $300 this year, $309 next year and so on – a geometric series. Over n years, I reckon you save 10,000(1.03^n – 1). That’s $3,500 over a decade, which isn’t bad at all 🙂

I appreciate your positive outlook. One person’s exponential growth is another’s exponential decay, I guess!