…putting money in the cookie jar

Putting money away is exactly what Obama doesn’t want you to be doing, although he’s far too tactful to say so directly.  But if you were the one to disobey El Obama’s non-orders, you may just be hiding rubles in the cookie jar.  As you can probably tell by his oversized pants, Obama doesn’t eat cookies… ever.

But if you, unlike purportedly-organic-produce-eating Barack, were to put away $1 every day in the cookie jar, at the end of the year, you’d have… $365 of course.  But with the possibility of inflation and cost of living increases each year, there are better things to do with your money.  Like…

…putting your money in a savings account

Now we’re doing a bit better. You’ve saved up $365 and realized that your cookie jar is better filled with Newman’s Own Organic Chocolate Chip Cookies.  So you’ve put the $365 into a 3% interest savings account, and you’ve even eaten some cookies, you devil…  And you earned interest! The formula for simple interest is:

SI = PV x r

Where SI is the simple interest earned.  PV is the present value (how much you deposit), and r is the interest rate.  So at the end of a year, the interest you earned is $365 x 0.03 = $11.  Congratulations!  You put your money to good use and earned $11 this year… not to mention the cookies enjoyed.

Inflation in the USA reduces the value of your money by something near 3% per year, on average.  So actually, all things considered, you just-about stayed even this year, and earned nary a cent.  Time to start thinking bigger by…

…earning compound interest in a savings account

Sure, you say.  I may have earned $11 last year, but that interest is going to be compounded, dollface!  What you mean is that the interest you made this year is going to be added to the principal amount you have in your account.  So next year, you’ll earn interest on the amount you deposited plus this year’s interest ($365 + 11 = $376), and the following year, you’ll earn interest on the interest you earned from that interest ($376 x 1.03 = $387), and after 10 years, you’ll be rich.  Poor sucker.

So, exactly how much will you have after 10 years?

FV = PV x [1 + (i / k)]n

Where FV is the “future value” of your money (e.g., the value after 10 years, in this example), PV is the present value (i.e., how much you deposit now), i is the annual interest rate, k is the number of conversion periods per year (how many times your money earns interest per year), and n is the total number of conversion periods.

In a typical savings account, your interest is compounded only once per year, so k = 1.  We want to know what the future value of your money will be after ten years, which in this case is 10 conversion cycles (ten interest cycles), so n = 10.  Our formula is thus FV = $365 x [1 + (0.03 / 1)]¹⁰

And that, my friends and fellow prisoners, is equal to $491. But you earned some compound interest!  To be exact, you earned:

CI = FV - PV

Where CI is the compound interest earned on top of principal amount you deposited.   FV is the future value, which in this case after 10 years we have just calculated to be $491.   PV is the present value, which is how much we originally deposited, i.e. $365.   So… after 10 years, you’ve earned interest of CI = $491 – $365 = $126.

As we established, with 3% interest, even if you had deposited $10,000, you would have just about kept up with inflation and earned almost nothing extra.. No matter how much you save, your 3% interest is doing nothing for you if inflation is wiping out your growth.  So what about…

…having an anxiety attack about inflation

Inflation is basically negative interest.  You can calculate the loss of value of your money over time due to inflation the same way you calculate its interest.

After one year of 3% inflation, your $365 has therefore lost $365 x 0.03 = $11 of value.  After 10 years, it has lost $126, using the same formula you used for calculating 10 years’ worth of compound interest, but using the rate of inflation (~3%, but varies each year)  instead of the rate of interest (also ~3% in our savings account examples).

If the interest you earn on your money is greater than the inflation rate for any given year, then you’re increasing the value of your money that year.  Otherwise, you’re just treading water at best.

With what we’ve already outlined, your children will be working at the pizza place in high school to pay off the hundreds of thousands of dollars in debt they will go through to get a decent education.  You should start thinking about…

…saving for your child’s education

So you’ve decided that, although your child, Wendy, will have to suffer the public education system, due to your negligence, you will at least offer with some sincerity to pay for her undergraduate degree at a state college.

New York state colleges go for about $20k per year, including room and board.  And, assuming your kid is one of the smart ones who get through undergrad in just 4 years, you’ll be shelling out $80k minimum.

Luckily for you, you don’t have kids yet.  It will be 20 years before your future kid goes to college. So you have plenty of time to start saving now.  How much should you put away in the bank right now in order to have enough to pay for her college?

FV = PV x (1 + r)n

Where FV is the future value, PV is the present value, r is the interest rate per conversion period, and n is the total number of conversion periods.

So the future value you want to have on hand in 20 years is $80k.  The annual interest rate, let’s say, is 10%, since you’ve figured out how to be very creative with your money, using bonds and stocks that earn more interest than than the standard bank savings account interest you had before.

So the future value, FV = $80,000, which is how much you want to have in the end; r = 0.10, which is the interest rate you can earn per year; n = 20, which is how many conversion periods (i.e., interest cycles) between now and when you want to have earned the money.

So, the formula above, in this case, looks like $80,000 = PV x (1 + 0.10)²⁰.  Solving for PV, we get PV = $80,000 / (1 + 0.10)²⁰.  In other words, PV = $11,891.  So if you invest $11,891 today at 10% interest per year, you’ll have enough to pay for your daughter’s undergrad education in 20 years.

But let’s be more realistic, and let’s say you can only find an investment of 5% per year… slightly better than a typical bank savings account.  That means PV = $80,000 / (1 + 0.0.05)²⁰.  With this interest rate scenario, using the same formula with an interest rate, r, of 0.05, the present value, the amount you have to invest today, is PV = $39,189.

Cancel that Tulum vacation this year.   But wait, you realize…. you won’t need the full $39,189 up-front.  Who says you need it all at once?  You can start making smaller payments every month that will contribute towards that final $80k goal in 20 years.  We’re talking a finite number of regular payments, not a lump sum.  You can still take that vacation.  You just need to start….

…contributing regular payments toward your kid’s education

So you’re poor and smart.  You’ve realized that you don’t need the whole shebang up-front.  You can put away savings every month until you save enough for the college expenses.   This is equivalent to a sinking fund.

You need to guarantee that 20 years from now, Wendy, your beautiful and chaste college-age daughter will be the lucky recipient of $80k to pay for college.  No doubt, she will fully appreciate the effort and sacrifices you’ve made in diligently saving all your profits of all your work every month in order to fund the development of her educated mind.

Let’s say you’ve again figured out how to earn 5% interest on your money, compounded yearly.  You’re getting better with your investments.  How much should you put away every month such that in 20 years you’ll have $80k saved up?  The formula linking future value, recurring payments, interest rates, and conversion periods is:

FV = R x [{(1 + r)n - 1} / r]

Where FV is the future value we are trying to achieve;  R is the payment you need to make each conversion period; r is the interest rate per conversion period.  and n is the total number of conversion periods.

In our case, FV = $80,000, the amount we want in the future; R, the recurring payment amount, is not known and is what we want to find out; r is 0.05, the annual interest rate, since we only have one conversion period per year; and n = 20, since we have 20 conversion periods: one for each year.   So the formula above looks like: $80,000 = R x [{(1 + 0.05)²⁰ - 1} / 0.05]

Rearranging this equation for R, we get R = $80,000 / [{(1 + 0.05)²⁰ - 1} / 0.05].  Solving this equation for R, we get R = $2,419  So you need only put away $2,419 every year at 5% interest for the next 20 years in order to have enough to pay for your daughter’s cheapo state college alcohol-hazed undergraduate education.

Since the interest on our money accrues yearly, not monthly, we just calculated how much we need to contribute to the fund each year.  We can always divide that number by 12 to get the necessary monthly contribution. $2,419 / 12 = $202 per month.

If we were able to find an investment that had conversion periods once every month, rather than once per year, then our interest would accrue 12 times per year.  We would have to modify our numbers a bit.  The more often the money accrues interest, the better.  With monthly conversion periods, the monthly interest rate, r, would be the annual rate divided by 12 months: 0.05 / 12 = 0.0042;  and n, the number of conversion periods would be 12 per year (one for each month), so n = 12 x 20 = 240.  The formula becomes: R = $80,000 / [{(1 + 0.0042)²⁴⁰ - 1} / 0.0042].  In this case, solving for R, the recurring payment every month would only have to be $194, which saves us $8 per month compared to the yearly interest payments.

Maybe you can afford to put away this amount each year.   Maybe you can’t.   Maybe you should start…

…putting away whatever pathetic amount you can muster to save each month

Let’s say you’re poor.  You can only afford to put away $100 per month towards your kid’s college education.   $100 per month is equal to $1200 per year.  How much will that measly amount be worth in 20 years?  Using the same formula as above, we have FV = R x [{(1 + r)ⁿ - 1} / r].

In our current example, we know the value of R, what we can contribute each year.  It’s $1,200.  And we want to figure out what FV, the future value, will be after 20 years of contributing this amount.  If we get an interest rate, r,  of just 5% per year, compounded yearly, we’ll again have one conversion period per year, so n, the total number of conversion periods, is 20.

Our formula is now: FV = $1200 x [{(1 + 0.0.5)²⁰ - 1} / 0.0.5].  Solving for FV, we get FV = $39,679.  So your deposits of $1200 every year will be worth $39,679 in 20 years at 5% interest.  This is about half of what we need to pay for our baby’s undergrad.  Pay double this amount, and Wendy will be ok.

If we can put away $500 per month, that equals $6,000 per year.  Using the same formula, the future value of $6,000 per year over 20 years, at 5% interest, is FV = $6,000 x [{(1 + 0.0.5)²⁰ - 1} / 0.0.5].  Solving this equation, FV = $198,396.  So putting away $6,000 per year for 20 years at 5% interest leaves your baby with $198,396 when it comes time for college.

Don’t worry, Wendy will be just fine.