# 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.

#### patrick honner

Math teacher in Brooklyn, New York

#### Fawn Nguyen · April 6, 2012 at 10:56 am

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

#### MrHonner · April 6, 2012 at 11:08 am

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 nothing about the current rent.

#### flyingcoloursmaths · April 6, 2012 at 11:28 am

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 🙂

#### MrHonner · April 6, 2012 at 11:54 am

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

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