Dear PoP – Who’s Good at Math?

by Prince Of Petworth November 8, 2010 at 2:30 pm 41 Comments

Photo by PoPville flickr user Bogotron

“Dear PoP,

This is probably more of a high school math assignment type of question – but I must have missed that day!  I’m the type that got straight A’s in college calculus but can’t compute a math problem needed for practical use! So, HELP — how do I do this??


DC Housing Regulations state that when a Landlord received a security deposit from a new tenant, that deposit should be placed in an interest bearing account (the total of which + interest ideally would be returned to the tenant in the future upon vacating the unit and assuming no deductions for repairs or damage would be taken).

OK, I admit I didn’t do that 13 years and 1 month ago. In Sept 1997, my tenant gave me $675 for a security deposit. I probably paid bills with it. Had I deposited that money in a dedicated interest-bearing savings account at that time, what would the account balance be today, attempting to account for daily compound interest? (I opened a new “Escrow Savings” account with my bank today to do this the right way with my new tenant. The daily compound interest rate today (Nov. 4, 2010) is 0.05%.)

a. If attempting to get by with estimating: Even assuming that the daily compound interest rate was the same for 157 months (13 years + 1 month) at 0.50% (which it was not)….but for argument’s sake say it was…..how do I calculate what $675 would be worth 157 months later at that rate?

b. If attempting to be accurate, is there an online calculator available that is already programmed with every daily compound interest rate since the beginning of time, enter an amount at a certain date and ask for a projected total at a specified future date? Or for accounting purposes, do they roll up daily compounded interest into a yearly average and plug in the formula 13 times….? _(*^&$^&

For me, this goes into the “too hard” pile, but I need to at least show my due diligence in making this calculation since I didn’t place the security deposit on interest like I should have done. What do other landlords do in this situation….or what would a law firm require should it be an issue? Thanks for your assistance!”

Oh man, my head just exploded. But I have faith in PoPville – can anyone do this calculation? Def. a free PoP t-shirt to whoever is first in getting a proper answer here.

  • Anonymous

    Here’s a calculator that can help you figure it out.


    Looks like about $720.

  • equan


    according to my excel calculations, it is $730.11

    (it’s a financial formula, you’re calculating for future value (FV))

    i’m terrible at math, but i took a personal finance course in college and it was the most useful thing in the world.

    hope this helps!

  • Anonymous

    Oh it’s way more than $720.

    I’m the kind of person who failed calculus but I’m pretty sure that this one involves the derivative of a natural logarithm (that funny e looking symbol).

    You’ve got even worse issues because interest rates haven’t remained constant for 13 years.

    I would just offer the guy $1,500 (you may actually still becoming out ahead) and see if he takes it. Seems like he’s been a good tenant.

    • Eric in Ledroit

      its a simple equation, not calculus.

      • Anonymous

        i’m pretty sure if you want to continuously compound you need an LN

        • Ragged Dog

          Nope. PV*(1-NT)^RT Or something to that effect.

  • Max

    THe answer is this is why there is a rental shortage

  • Eric in Ledroit

    Interest rates now are at historic lows because of the financial situation in the country. You should assume something like 2% or 3% annual interest for a 13 year period.

  • skeedattle

    Agree with Anon @ 2:43. Rates are currently at historic lows. Look at the historical fed funds rate by month to see the trend. Fed funds rate for Oct ’10 was 0.19%. For Sept 19 it was 5.54%. Much higher. $1,500 could be a bargain. Here’s a list of historical fed funds rates from economagic.com: http://www.economagic.com/em-cgi/data.exe/fedbog/fedfund

    • skeedattle

      Sept 97, not Sept 19

  • Noah

    Was your tenant Lester Freamon?

  • equan

    woops! that was with the current interest rate you gave (.05). with a .5% interest rate the total will be:

  • Tres

    $1010, roughly. I used a website that calculates your future value today, given having made a deposit X number of years ago.


    You have to check the “short term” savings box only, so it uses rates that banks would have given you. It also does historic stock returns and gold.

    • jcm

      You win.

      • Tres

        Finally, something fine enough to wear while bestride some yaks in Peru.

  • heffieb

    The formula for compound interest is E=P(1+r/n)^(nt), where E is the ending amount, P is principle, r is the interest rate, n is the frequency of compounding, and t is time. For this scenerio and using the same 5% interest rate over the entire 157 months, you get E= 675(1+.05/365)^(365(157/12)), so if $675 principle had been compounded daily at 5% for 13 years and one month, it would be worth $1298.33 today.

    • skeedattle

      That only works if the interest rate is fixed.

    • Tres

      My calculator uses historic data. ;)

      • heffieb

        True, but it doesn’t compound daily. Any site that lets you play with gold is good though. :-)

  • heffieb

    Right, but that was one of the given assumptions. Working in a different daily rate for 13 years would be beastly. If another fixed rate would come closer to averaging out over time, it could readily be plugged into the equation.

    • skeedattle

      :) i think the beastly nature of the problem is why the reader posed the question.

  • anne

    I believe it’s “simple interest” not “compounded” and I think DC requires minimum 5% interest — it was passed when interest rates were over 10%. So I think who ever said $1010 is close.

  • soners

    The equation you are looking for is

    deposit*e^(yearly interest rate*number of years)

    so in this case


    (I translated your .05% daily compound rate into a yearly interest rate of .5%–you could probably get 1% right now, but .5% is reasonable).

    To adjust for past higher rates, I would probably do a really rough rounding. According to this
    Interest from 97 to 01 was roughly 5% so for those first four years:
    The next 3 years were around 1.25
    824.44e^(.0125*3)= 855.94
    The next three years were around 4.4
    And the next 2.083 at 1%

    Obviously you could use the table and some excel to do a year by year but $1000 looks pretty close.

  • Park View Drew

    Wait a second… I assume that at the time you gave him back the deposit without interest right?

    I’m not an expert on the law here, but I can’t imagine you owe him interest on the full value.

    If you gave him back $675, and you really should have given him back $700 (interest included), you should only be paying interest on the $25 difference (<$100 by any reasonable estimation).

    There may be some penalties involved, but that's another issue.

    Also, why is this only coming up 13 years later?


    • jcm

      The law says the landlord has to pay interest for the time he’s holding the deposit. So he took $675 13 years ago, and needs to return $1010 today. Here’s the actual law:

      The interest in the escrow account described in § 309 on all money paid by the
      tenant prior to or during the tenancy as a security deposit, decorating fee, or similar
      deposit or fee, shall commence on the date the money is actually paid by the tenant, or
      within thirty (30) days after February 20, 1976, whichever is later, and shall accrue at the
      passbook rate then prevailing on January 1st and on July 1st for each six (6) month period
      (or part thereof) of the tenancy which follows those dates. On those dates, the passbook
      rate in the District of Columbia financial institution in which the escrow account is held
      shall be used.
      311.2 Interest on an escrow account shall be due and payable by the owner to the
      tenant upon termination of any tenancy of a duration of twelve (12) months or more,
      unless an amount is deducted under procedures set forth in § 309.

      • Park View Drew

        Right – If he kept $675 for 15 years. But the original post wasn’t really clear about that.

        I took it to mean that he paid back $675 but didn’t pay the year’s worth of interest (call it $25 for the sake of argument).

        In that case, I think he only owes 13 years of interest on $25, not on $675.

  • Herb

    I was in banking for over 20 + years so let me provide you this calculation–with interest the account value should be about $1100. From that you should subtract 13 years of a monthly service charge of $5.95 for falling below the monthly minimum balance plus 10 years of a dormant account fee @ $7 per year plus a $ 50 closed account fee and $8 to issue a bank check so basically your tenant owes you $43.80.

    You are welcome.

  • Eric

    Can we get a regulatory citation. I know the VA housing regs stipulate a minimum rate (2009 was 0% cause of deflation) but its wierd that they dont stipulate anything. Remember, some savings accounts are like 0.25% currently, and they have been really low like that for years.

  • Anonymous

    As a fellow landlord, I think the answer is simple: if you intend to pay back the full deposit to this tenant, write a check for $675 and call it a day. If your tenant complains about it or asks where the interest is, deal with it then. (For what it’s worth, I’ve always kept the deposits in a DC-located, interest-bearing account, as required. On a much higher deposit than your $675(between 1600 at the start to the current 4500+), for almost 7 years, the account has made something along the lines of $25 in interest. You are way overthinking this if you conceptualize it as a math problem and come up with a number in the 1000s.)

    • Anonymous

      PS — Even if your tenant is a complete stickler, I think you’ll find that the amount of interest is not nearly enough to incentivize your tenant to take you to court for it. It’s not worth anybody’s time. And if you really feel bad about it, cut him an extra $200 as a long-time tenant “rent refund,” tell him you screwed up as a jr. landlord and hope that is a good-faith cover of the interest not earned, and really appreciated that he was a good tenant. Honestly, you’re talking about the lowest amount of interest possible — a bank-based savings account. No one can expect that deposit doubles as a long-term investment.

      • Tres

        If I was a tenant, I’d sure as hell take the landlord to court — even if it was for measly $100. I’d encourage others to do the same. Use a sick day, and you just made an extra $100 over your normal daily salary — a nice dinner for you and your +1. But the sweetest part will be that the landlord has to show up, lose a day of their life, and suffer public disgrace. Oh — and hopefully learn a valuable life lesson.

        That said, the threat of a lawsuit is usually all you’ll need. The threat is strong enough to force compliance — so in the most likely scenario you don’t even have to take off work. Send the landlord a respectful email delineating the consequences of their withholding your interest. Give them a short deadline to settle out of court. They might hand deliver the check the next day.

        • Anonymous

          I’d suggest you’re a far outlier in this regard. It’s not just a day for $100 — you still have to file the case, serve the complaint on the landlord, etc.. (And even then, you probably couldn’t pay me $100 — or $200 or $300 — to voluntarily spend a day in DC Superior Court.) But you’re right — no way the landlord just wouldn’t pay something and make it go away.

          But that’s beside the point here. The fact that this landlord took the time to think about this and ask the question shows he wants to do the right thing. Based on that and the 13+ year landlord-tenant relationship, it’s an educated guess that there’s actually a pretty good relationship between the two of them and a “let’s work it out” solution to be had. My suggestion primarily is that it can be resolved amicably and in good faith with a sensible solution. He basically admits liability, and the question asked is one of damages. But I’m willing to bet that, were you to attempt to litigate the issue of interest in small claims or landlord-tenant court on an amount that small for a 13 year period, the judge would order some nominal amount that he pulled out of thin air and tell you to save your breath. It’s a waste of everybody’s time, and a public waste of time to get the courts involved, if you can just agree on something that’s acceptable for both sides. Honestly, 7 years on an interest bearing account in DC with 3-6x this amount of principal, and the interest is a total of $79.92.

  • carn

    I laugh that someones even figuring this out. Having just been through the small claims process in our lovely city.. I would LOVE to see someone show up to court and hand the judge a bunch of paperwork and math computing historical compound interest rates. Hopefully this is right after the bailiffs tackle the 300lb woman for decking another woman over her “motherfuckin 30 dollaz” and before the case where the judge yells “DOES ANYONE SPEAK GODDAMN ENGLISH IN THIS ZOO ANYMORE!?”

    • Anonymous

      oooo…more details please!!!

    • Anonymous

      Ha ha. I 100% concur. Yet again, this email demonstrates the absurd chasm that exists between people in DC to whom the law means something and those to whom it does not.

      I think OP is completely admirable and upright. He deserves good landlord karma from this point forward. May he never get anything less than a Martha Stewart-clone as a tenant. But what a waste of mental energies to give this another second of thought, especially in a town where kids shoot each other for nothing and people can stay 6 months in a rental, under the protection of the law, without paying a cent in rent.

  • just take him out for a nice meal at Popeye’s and call it even! mmmmmm

  • Recent Plantiff

    I was in a situation where a landlord was trying to fleece me out of a few hundred dollars of my deposit. After filing papers (a tenant petition, not a small claims suit), we went to a mandatory mediation where I recovered almost all of my money. I would have gladly skipped the whole thing if my former landlord had worked with me to come up with a solution. It sounds like this is not a contentious situation, so don’t make it contentious. I would offer around $1000 in total (interest rates were pretty high for a few years in there and I think the old law requiring 5% interest might be in effect since that was the law back in 1997). If my landlord had acknowledged that he spent my money (the deposit is the tenants money that you are supposed to be holding for him) and tried to pay me back reasonably I would have avoided court. If you keep acting in good faith I bet he will work with you.

  • landlord

    Are you sure you are actually required to keep the deposit in an interest-bearing account? I thought that only applied to landlords renting over a certain number of units. Like rent-control regulations only apply if you own more than 4 units.

    • quincycyclist

      Yep, you are required to regardless. Of course at today’s interest rates you’re looking at like $10 on $1000 deposit, so…

  • Don

    Excellent discussion! Allow me to chime in as a financial planner and bring some order to this discussion.

    There’s a few assumptions that need to be taken into account with respect to this problem. First, heffieb’s calculation of $1,298.33 (I calculated $1,298.34) is dead on, based on a daily compound rate of 0.000137% (5% / 365) as the following factor (1 + 0.000137)^4775 (the number of days in 13 years, 1 month) = 1.923469 X $675 (security deposit) or $1,298.34. This is in line with the the quick Rule of 72 where you take 72 / 5 (assumed interest rate) to determine that money doubles in approximately 14.4 years so the answer is closer to $1,350 in 14 and 1/3 years.

    Problem is, §311.1 of Title 14 of the D.C. Code (DC Housing Code) states that “The interest in the escrow account described in § 309 on all money paid by the tenant prior to or during the tenancy as a security deposit, decorating fee, or similar deposit or fee, shall commence on the date the money is actually paid by the tenant, or within thirty (30) days after February 20, 1976, whichever is later, and shall accrue at the passbook rate then prevailing on January 1st and on July 1st for each six (6) month period (or part thereof) of the tenancy which follows those dates. On those dates, the passbook rate in the District of Columbia financial institution in which the escrow account is held shall be used.” Passbook savings rates in 1997 loomed at around 2% (give or take) and have not risen much above in the proceeding 13 years. Therefore, using 2% as a constant savings rate for the period, the answer becomes (using annual, not daily compounding as in the above calculation):

    PV(1 + i)^n
    $675(1 + 0.02)^13.0833

    Just my two cents worth (no pun intended).

    • Tres

      Very interesting. I feel like we all learned something.


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