Learn To Be A Compounding and Discounting Cashflow Wizard – Including Book Excerpt

Editor’s note: This post first appeared in Make Change magazine, an online personal finance site.
Interest rates don’t seem like a crucial thing to learn about in your 20s or 30s. And learning the seemingly-complicated math of interest rates – specifically compound interest and discounting cashflows – might not seem like an accessible or important skill. Oh…but they are. One reason why I insisted on teaching this math in the early chapters of The Financial Rules For New College Graduates: Invest Before Paying Off Debt And Other Tips Your Professor Didn’t Teach You is that we need to demystify finance. I mean, it’s not a magic trick. Financial professionals are not wizards. They really don’t deserve to be paid as much as we pay them. You can learn this by opening up a spreadsheet and watching a few embedded videos here. With a little effort you should end up knowing it better than 99% of people. Better than most financial professionals, for that matter.

wealth_monorailIt starts with understanding simple interest, and we build from there. You probably know that if you borrow $1,000 from a buddy for a year at 8% that you will have to pay back $1,080 at the end of the year. In that sense, interest on money that you’ve borrowed means you have to work extra hard to earn enough every year to pay off your debts. The higher the interest rate, the harder it becomes. Like owing $1,000 on a credit card charging 22% in interest creates an even harder headwind, costing you something like $220 on the $1,000 debt. That interest rate is like a backwards moving monorail, against which is it hard to get ahead, when you’re in debt.

But interest rates, as I explain in my book, can work in your favor as well:


But here’s an optimistic thought: The monorail also moves the other way. Interest rates on your money—also broadly understood as Yield and Return—can move you forward. When interest rates work in your favor— specifically when you are a lender or an investor— your money today grows into larger amounts in the future without you hardly even trying.

For wealthy people, money they have today for investment simply grows into larger amounts of money tomorrow. They can choose a slow-moving and safe monorail, historically earning 1 to 3% annual return, or they can choose a more volatile but ultimately faster monorail, earning above 5% per year. Done correctly, this wealth-building requires little skill or effort.

I use the monorail metaphor to understand this phenomenon because wealthy people with the right approach to investing cannot prevent themselves from having more money in the future. Just by standing still. Just by doing absolutely nothing. Money just grows on money, pretty much all by itself, if we can get ourselves out of the way and let it.

I hope to inspire you to examine whether the monorail you are currently on— the interest rates that affect you and your money— moves you forward or whether it moves you backward. I hope you embrace the optimistic thought that even if right now you find yourself working twice as hard just to stay in one place on a backward-moving monorail, you can flip that switch. In the future, you could let yourself be propelled forward by the same monorail.


The mathematical power of flipping that switch is captured in the concepts of compound interest and discounting cashflows, which I’ll introduce and explain further in subsequent posts. As a preview though, I think the following two ideas we gain from compound interest and discounting cashflows are worth thinking about:

Compound Interest: If we managed to scrape together a nest egg amount of $5,000 to invest in an IRA at, let’s say, age 25, we could invest that for the long term, let’s say for 40 years until retirement age, at 65. If that $5,000 earned a compound return for 40 years at the reasonable rate of 6%, it would be worth $51,429, rounded to the nearest dollar. If it compounded for 50 years until age 75, at the high (but historically plausible) rate of 10% annually, it would be worth $586,954. That’s potentially life-changing. And it’s not magic or wizardry. It’s math. It’s demonstrable when you learn compound interest math such as in this embedded video:

Discounting Cashflows: If we knew we wanted to have a retirement portfolio of $1,000,000 at age 65, and thought we could achieve a 6% return between now (age 25) and then, this math concept tells us we’d need a nest egg today of $97,222 rounded to the nearest dollar. If we could achieve an 8% return, we’d only need a starting amount of $46,031. That’s a solid but not outrageous amount of money to gather together in one’s 20s. The math required to do that calculation is introduced in this embedded video:

This is really what understanding interest rates, and interest rate math, helps us do.

Please see related posts:

Introduction to Compound Interest with Book Excerpt – part 2

Introduction to Discounting Cashflows with Book Excerpt – part 3

And buy my book here: The Financial Rules For New College Graduates

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A Stock Growth Miracle (Not Really)

Psst: Do you want to hear about a neat investing trick a family friend showed me? She started with $250. Through alchemical magic – well, a mixture of time, compound interest, and an important dash of negligence – she turned that $250 into an investment today worth $135,000. She still owns it, so results may vary in the future, but her gains are amazing.

I imagine you’d like to learn her trick. How ever did she do it? What financial wizardry did she employ? It was probably Bitcoin, right? Or some lesser known cryptocurrency? Or a hot commodity tip?

My friend requested I not identify her. I’m going to call her Ruth, although that’s not her real name. That’s her mom’s name.

The story starts in 1965. Ruth was newly married. As much as possible, I’ll let her tell it:

“I lived in the State of Washington, and my grandmother used to buy stocks, even though she was a middle-class person. She thought it was good to buy local, and Seattle was dominated by Boeing Co (BA).”

“At that time people thought you were supposed to buy 100 shares of everything. I didn’t have enough to buy that amount, so I bought less than that initially.

I invested around $250 at the time…It was probably 20 shares, no more than 40. I remember the broker criticized me for not buying 100 shares.”

compound_interestOk, that’s the beginning of Ruth story. Are you ready for the magical part? Then Ruth did nothing for 53 years. That’s it. That’s the whole magic.

Never sell.

In 2018, her initial $250 investment in “20 or 40” shares of her local company Boeing has turned into 400 shares through stock splits and the reinvestment of dividends. Her initial investment is worth, at the time of this writing, $134,800. Through Ruth’s benign neglect. The dividends alone on her shares pay around $2,700 per year, or more than 10 times her original investment.

At least three important lessons and clarifications of the lessons of Ruth’s story are necessary.

First, this is the story of a particular investment in Boeing that happened to be headquartered in Ruth home state, but you could substitute hundreds of successful companies from 1965 into that same story, with similar results. The point is not “I wish I’d bought Boeing in 1965,” but rather “I wish I’d bought a tiny amount of shares of any number of successful companies, and then done nothing further, for 53 years.”

Second, I was kidding earlier about magic, just to get your attention. This is actually the most normal thing in the world.  Turning $250 into $134,500 over 53 years is not magical at all, but rather a mathematical result of time and compound returns. To be precise, Ruth’s initial investment – through reinvestment of dividends, splits, and stock price gains, grew on average 12.6 percent per year for 53 years, from 1965 to 2018. And that’s a good return. It’s above average.

But it’s not ridiculous for a successful US multinational company from that period to today. The annualized return from the S&P500 since 1965, including reinvestment of dividends, was 9.87 percent. If it had been technically feasible to invest $250 in the S&P500 in 1965 (note: it wasn’t realistically possible then) and then let it compound for 53 years, the stake would be worth $36,689. That’s not as cool as Ruth’s $134,800, but it ain’t nothing either.

Third, Ruth is no genius investor. She’s pretty typical. The really funny thing is that while she told me her story, she continuously bemoaned her lack of investment savvy.

“I feel embarrassed talking about Boeing because I could tell you about a lot of mistakes, and even stocks that went to zero.” Which is charming, and no doubt true, but doesn’t negate her success. Remember: She turned $250 into $134,800. (Psst.If you are still in your twenties, so could you. Start with $250. Then do absolutely nothing for 50 years or so. That’s the hard part.)

Also, the part of the story I didn’t tell you yet is our whole conversation started because Ruth had initially described to me selling 500 shares of Boeing in the beginning of 2017. She’d bought those particular 500 shares at some point in the 2008 crisis. She saw a market price of $175 per share in February 2017 and thought to herself: “That can’t go any higher.” Nearly a year later the price has almost doubled. Ruth was kicking herself in the initial part of our conversation for that sale a year ago.

“I know I’m doing it wrong, when the price goes up and I’ve already sold, and I could have sold at a higher price. It’s not the first time it’s happened…It’s hard to know how to time a sale.”

She wanted to know when was the right time to sell. She felt like she blew it as an investor.

boeing_stockAlso, she’d been tempted to sell a lot earlier.

“Sometime a few decades ago my husband and I talked about selling our stake in Boeing, taking the money out and building a swimming pool. Our whole stake was worth $30,000 and we thought it couldn’t go any higher.”

“How do I know when to sell?” she asked me, probably four or five times in our conversation. “Never,” I answered each time, or some variation on “never.” But still Ruth wanted to figure out how to properly time the market. Which is impossible. Ruth feels like she gets a lot of things wrong with her investing.

It’s better to be lucky than good we always say on Wall Street, and of course Ruth got lucky buying a small amount of the world-class stock from her home town. But she was also good, in that she didn’t sell that stock for over 50 years.

Stock Disclosure: I own zero Boeing stock, and zero individual stocks for that matter, preferring to invest in equity index mutual funds. And so should you, for that matter.


Please see related posts:


Never Sell! as Churchill would say, if he were a stock investor

The magic of compound interest

Video: Compound Interest – A Deeper Dive


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Discounting Cashflows – A Deeper Dive

Welcome! This post is meant to accompany Chapter 5 and Appendix to Chapter 5 “On Discounting Cashflows” in my book “The Financial Rules For New College Graduates – Invest Before Paying Off Debt And Other Tips Your Professors Did Not Teach You.” (Praeger, April 2018.)

I’m convinced the only way to really learn discounting cashflows math is to practice with a spreadsheet. The only way to gain intuition about how this math is used in the real world – how it can help you build wealth – is through a bit of spreadsheet practice.

In this first video I show how to build a simple calculator for determining the present value of future cashflows. This is the fundamental math used in investing in assets such as stocks and bonds. It’s also how we would value everything from annuity payments to pension payments to public liabilities.

In this second video, I show how to discount more than one cashflow. The key point is that each separate future cashflow needs it own discounting formula.

The next video shows how to discount cashflows using other-than-annual discounting rates. This is relevant because in the real world cashflows don’t just come once a year. They could be semi-annual (like a bond) or quarterly (like a stock) or monthly (like debt payments). We need to adjust our calculation by adding one extra variable – the number of compounding periods per year – as I show in this third video.

Learning how to discount cashflows can get more complex from here, especially for finance professionals, but the basic math shown here is both within the grasp of non-finance professionals as well as applicable to many important personal finance situations.




Please see related posts:

On Compound Interest – A Deeper Dive

Book Review: The Intelligent Investor by Benjamin Graham


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Compound Interest – A Deeper Dive

The_Financial_RulesWelcome! This post is meant to accompany Chapter 4 “On Compound Interest” and the Appendix to Chapter 4, in my book The Financial Rules For New College Graduates: Invest Before Paying Off Debt and Other Tips Your Professors Didn’t Teach You (ABC-CLIO Praeger, 2018.)1

I highly recommend you open up a spreadsheet alongside this material.

For starters, we want to know how to set up a spreadsheet to calculate Future Value, if we already know Present Value, Yield, and Time.

This first video below can get you started on that journey.



The next video adds a level of complexity. Let’s say we want to see multiple years’ worth of compounding returns. For example, we might want to contribute to a retirement account multiple years in a row, and see the results of that activity over time. Spreadsheets are ideally suited for this type of setup, as the next video shows:



The third compound interest video introduces the idea that in the real world, money can compound more frequently than annually. Bonds often compound semi-annually. Stock returns often compound quarterly (because dividends are paid quarterly.) Monthly-pay debts we owe to our mortgage company, credit card company, or auto-loan company compound 12 times a year. We need to add an additional step for compounding more frequently than once a year.

Please see related posts on Discounting Cashflows and Compound Interest:

Discounting Cashflows – A Deeper Dive With Video 


And please see my earlier writing about compound interest and discounting cashflows.

Compound Interest – The Most Powerful Math in the Universe

If You Like Feral Cats, You’ll Love Compound Interest

College Savings And Compound Interest

Rapunzel and Compound Interest

Compound Interest and Vampires


How To Win With Powerball – Learn The Discounting Cashflows Math

Discounting Cashflows – Annuities

Discounting Cashflows – Pensions



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  1. Hey! Order it here: https://www.amazon.com/gp/product/1440861056?ie=UTF8&tag=bankeanony-20&camp=1789&linkCode=xm2&creativeASIN=1440861056

Ask An Ex-Banker: The Magical Roth IRA

A version of this post ran in the San Antonio Express News.

Dear Michael,

Next January, when I receive the proceeds for a house I’m selling, I’m considering converting 70K from my TIAAF-CREF Traditional IRA into a Roth IRA, and paying taxes to do that that. I could then make my 7 grandchildren the beneficiaries and plan to not spend any of the Roth IRA myself unless I was desperate. I am 72 years old now, and my seven grandchildren range in age from 4 to 18. Could you make a spreadsheet to show me – and them – how nice that would be for them if I died at 90 and they received tax free income until they are all age 72 themselves?

Julie from Massachusetts


Dear Julie,

Thanks for your question. You’ve highlighted one of the cool and little-discussed features of the Roth IRA, a potentially magical low-cost estate-planning tool for passing on tax-free income to young heirs.

The Roth IRA magic I’m about to describe happens because of three features unique to Roth IRAs.

First – unlike a traditional IRA – all withdrawals from an inherited Roth IRA are tax free to the beneficiary. Roth IRAs, we recall, require income taxes to be paid up front, either when a contribution is made, or in the case of Julie, when an existing Traditional IRA converts to a Roth IRA.

Second – also unlike a traditional IRA – you are not required to make any withdrawals from your Roth IRA in your own lifetime. If you can manage to survive without pulling out money from your Roth – as Julie referenced in her question – then you can leave that much more money for your heirs.

Third – heirs can withdraw money slowly enough from their inherited Roth IRA that their little nest egg can actually grow over time. The IRS has a schedule for inherited IRAs that shows how to calculate just how slowly money may be withdrawn.

By exactly how much money will the grandchildren benefit, and how does it all work?

Tax Free Inheritance!

The total value

I’ll take Julie’s example and run through the numbers, but let me hit you with the punch-line first:

Julie’s nest egg would produce nearly $1.2 million of tax free income for her grandchildren.

Here’s some fine print on that punchline: $1.2 Million of tax-free income assumes Julie starts with $70,000 next year; She dies at age 90; all of her grandchildren take only their minimum distributions until they turn 72; the accounts earn 6% per year; and each grandchild receives the total remaining value of their inherited Roth IRAs at age 72.

If I keep all of those above assumptions, except I dial down the annual return to a more conservative 3% return per year, her grandchildren receive $273,054 in total tax free income.

But what about the following?
If I dial up the annual return to a more optimistic 10% per year, her grandchildren would receive a total of $9.2 million in tax free income. 1

Now that I have your attention, how does the Roth IRA achieve this magic trick?

The magic happens over two phases, Julie’s life, and her grandchildren’s lives.

Julie’s Life

Traditional IRAs 2 require an owner to withdraw a portion of their retirement account as income every year after age 70.5. The IRS publishes a list for IRA owners age 70.5 and older about their required minimum distribution, roughly determined by the retiree’s expected remaining lifespan.

According to the IRS, A 72-year old like Julie would be required to divide the value of her IRA by 25.6 (the same divisor goes for all 72 year-olds), and take at least that amount out of her traditional IRA as income. 3

With a $70,000 Traditional IRA, Julie must withdraw at least $2,734.38 at age 72, (because that’s $70,000 divided by 25.6).
With a $70,000 Roth IRA, however, she is not required to withdraw anything.

If Julie is able to survive on rice and beans (and Social Security, and other savings) without drawing from her Roth IRA, the account will certainly grow for the next 18 years. At a 6% annual growth rate, her Roth IRA would reach $188,494 when she reaches age 90. At which point we assume each of 7 grandchildren inherits a Roth IRA worth $26,928 (because that’s $188,494 divided 7 ways).

The grandchildren’s lives

An inherited Roth IRA requires an heir to make minimum withdrawals, but in small amounts determined by the age of the heir. The minimum withdrawal amount is determined by the value of the Roth IRA divided by the expected lifespan of the heir.

The key here to the Roth IRA magic is that Julie’s grandchildren are relatively young, and the IRS allows young people with a long expected lifespan to withdraw money from inherited IRAs quite slowly.

So slowly, in fact, that each grandchild’s account is likely to grow over time, under reasonable annual return assumptions.

The eldest grandchild
Julie’s eldest grandchild, now age 18, would be aged 36 when Julie is 90. The grandchild could elect to take the inherited $26,928 all at once, but would be advised not to do so.

Instead, she should allow the account to grow over time, kicking off a growing amount of tax free income per year over the course of her lifetime.

At age 36, the eldest grandchild has an expected remaining life of 47.5 years, so could elect to take the minimum of tax free income of $555 (because that’s $26,928 divided by 47.5).

With that minimum withdrawal, assuming a 6% return, the account will grow each year. Withdrawals will increase each year as well, up to $4,136 when she is 72 years old, when the account will be worth $67,424.

The youngest grandchild
For the youngest grandchild, the deal is even sweeter. She would inherit $26,928 at age 23. Her original minimum withdrawal of tax free income would be $448 (that’s $26,928 divided by her expected remaining lifespan of 60.1 years). Minimum withdrawals would grow up to as much as $7,090 by age 72, at which point the account would be worth $109,903.

The younger the heir, the higher the potential for maximizing this Roth IRA magic, which can produce tax free income for life, long after the original retiree has passed.

In the most optimistic scenario, if markets return over the next 100 years at the rate they have in the past 100 years (a key “if”) Julie’s conversion of her relatively modest $70K Traditional IRA into a Roth IRA would produce close to $10 million in future tax free income for her grandchildren.



Please see related posts:

The Magical Roth IRA

Estate Tax – My Problems With It



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  1. Incidentally, even though past performance is not indicative of future results, the S&P500 (including reinvestment of dividends) has earned 11.7% over the past 40 years.
  2. Just like other retirement accounts such as 401Ks and 403bs
  3. As a retiree ages and her remaining lifetime shortens, the IRS requires the retiree to divide by a smaller number, leading to higher distributions. A 90 year old must divide her traditional IRA account value by 11.4 for example, so would have to take out a minimum of $6,140 on a $70,000 account (because that’s $70,000 divided by 11.4).

If You Like Feral Cats You’ll Love Compound Interest

A version of this post appeared in the San Antonio Express News.

feral cats

Nobody ever told me this, but I’ve always assumed that a first rule of writing is to never – ever – try to teach math through blog posts.

But I learned writing through blogging on the interwebs where a first rule of everything – always – is to involve kittens.

Today I would like to teach the compound interest math formula using the story of the feral kittens in my backyard.

Compound interest is the most important, most powerful, and never-taught financial concept in the universe. Compound interest is also how middle-class people can get rich slowly and inevitably, over a lifetime of ordinary earnings.

Please bow your heads with me. Forgive us, editors and readers for the math we are about to learn. Also, hey look, kittens!

Start with just a few kittens

When you start with a small number of feral cats – as I did in my backyard recently, and then neglect to ‘fix’ them right away – pretty soon the magical compounding power of the universe goes to work.

It feels like one day I noticed a couple of stray cats, then I blinked and went out for a cup of coffee, and suddenly my entire yard was overrun with the things.

How does this happen?

Just ignore their gawdawful screeches at 3am, and boom! 2 months later, you’ve got more kittens.

Mathematically, I can tell you precisely how it happens, using the “compound growth of kittens” formula. It’s a matter of gestation periods which I’ll call “N”, and a growth rate per gestation period, or “Y.”

I can haz compound interest?

Using the compound growth formula in practice

I start with two kittens.

(Important note: they must be different genders for the math to work. I’ll spare you the science behind that assumption. Just trust me on this point.)

Let’s say we know that kittens multiply at a rate of 20% per gestation period. And let’s say I wait three years – that’s 18 gestation periods, since cat pregnancy lasts 2 months.

(By the way, all you animal experts and cat-lovers out there who have their claws out to correct me on these assumptions, please recognize: This is all a feline metaphor and not guaranteed to be biologically accurate. Thank you.)

So like I said, my N is 18, and my Y is 20%.

With those assumptions, I can tell you precisely how many future kittens we’ll have, using the compound Kitten Growth Formula.

Here’s the math formula:

The future number of feral cats equals “1+Y,” raised to the power of N gestation periods, all multiplied by the original number of cats.

For algebraically-inclined folks, we would write this kitten-growth formula “Future Number of Kittens equals Original Kittens * (1+Y)^N.”

Plugging my assumptions into the formula:

The future number of feral kittens I can expect in three years (all else being equal)[1] must be (1+20%)^18, multiplied by my original 2 kittens.[2]

So, my compound kitten formula tells me that at the end of 3 years I can expect to have 53 cats. Absolutely swarming all over my backyard! Excuse me while I sneeze just thinking about it.

All of you readers following my math so far (seriously, both of you!) should try that out with a spreadsheet. When you change the percent kitten growth rate Y, or the number of gestation (compounding) periods N, you can see how the future number of kittens changes.

For example, if you start with four “Original Kittens,” and they grow at a rate of 25% per gestation period (that’s Y), and you neglect them for 5 years (so N=30 two-month gestation periods) then you can expect 3,231 kittens in your backyard. Roawrrr!

These are a few of my favorite things

What about money?

Ok, back to money.

This compound growth formula is the key to understanding the importance of long-term savings and investment.

Allow me a few quick mathematical statements that you can prove to yourself on the spreadsheet you’ve taken out, using the compound interest formula.

Remember, your Future Money is just going to be “1+Y,” raised to the power of N, multiplied by your Original Amount of Money.

Hey, that’s weird, it works just like cats!

So, if you are 25 years old, and if you have $5,000, and if you can earn 7% on your money for the next 50 years (I understand, a lot of “ifs” but bear with me on the math part, because this can change your life for the better) you will have $147,285 in your account when you are 75.

Without you doing anything to your money, just neglecting it like a feral cat.[3] And $5,000 is just one years’ worth of contributions. Imagine making multiple years of retirement contributions when you are in your 20s.

If you buy a $200,000 house, experience 3% home-value inflation and live in that house for 40 years before selling, your house will be worth $652,407 when you sell.

Partly I’m mentioning these things because they illustrate, mathematically, how middle class people can build wealth slowly and inevitably.

More than partly, I’m hoping readers will be inspired to open up a spreadsheet and learn to use this formula to estimate the future value of their money. Or their future number of backyard feral cats, if they prefer.

Gratuitous catwoman picture

In real life, since you asked, I noticed a couple of feral cats in my backyard last Spring. By this Winter, we had eight. A neighbor with great cat-catching & fixing skills (Shout out to Cannoli Fund!) caught and fixed all eight for us. Thank goodness for my neighbor because that cat growth curve was about to hit the stratosphere.


[1] As an economist would say. Although an economist would insist on say it pretentiously in Latin, with the exact same number of syllables, thus saving no time at all, but giving the illusion of fanciness: “ceteris paribus”)

[2] By the way, always use a spreadsheet when using compound growth formulas. Don’t simply try this with your catculator. Ahahaha! Catculator! I’ll be here all week folks. Don’t forget to tip your server. And try the fish.

[3] Picture your money, multiplying itself at 3am, while you (try to) sleep. Strangely, dreaming about Anne Hathaway in the last Batman movie.



Please see related post:

Compound Interest and Wealth

Compound Interest, Blood, Lust and Vampires – guest post by The Banker’s Wife

Rapunzel and Compound Interest

College Savings and Compound Interest


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