Think of those moments for a second. Customer email. Customer phone. Customer face-to-face. Customer enquiry. Customer complaint. Customer invoicing. Customers on social networks (Facebook, Twitter).

There are a huge number of situations where your business has an opportunity (where the rubber meets the road) to put a comforting hand on the customers’ shoulder for reassurance, support and to remind them that you exist.

So you can look at those points strategically and ask yourself what experience, what impressions, what outcomes arise from each of those touch-points? How can you, the business, create value or maximise the customer’s impression of your business (product / service)?

Was the customer offended and treated with dignity? Did the representative at the counter trash the company brand by being curt or petty? Was there an opportunity to use the touch-point as an up-selling or cross-selling opportunity. Could you develop relationships? Could you put coupons or theatre tickets attached to certain invoices as a reward program for continual prompt payment?

Here’s a classic e-marketing example. Somebody registers on your website (a touch-point) and leaves an empty shopping cart with two books (another touch-point). The following week, if the cart remains idle, you could reach out and remind that registered customer that they haven’t revisited the cart – maybe they’re interested in something related, perhaps they were absent-minded? If the cart remains idle, two weeks later you reach out and touch them again to raise awareness of a special deal. One month later you reach out and simply say we appreciate the opportunity to do business and hope they return for the Summer / Winter / Easter Sale.

It’s certainly a different way to look at your business. Rather than seeing it as a simple transaction in the marketplace you refocus onto all those touch-points and hone them into a great experience for the customer. The email gets answered within hours, not days. The social media comment is responded to intelligently – even when it is critical of your mistakes. You continually try to value-add, enhance and influence the minds of the market.

And you do this strategically. You sit down and codify the lot so that you know the exact response time for each touch-point. If you receive a complaint it ceases to be arbitrary… the response is courteous, appreciative of feedback and, if valid, the customer gets some free service or product or other opportunity that will turn them around.

Because those touch-points are the opportunities that allow you to go one-to-one with potential and existing customers. This is where you look them in the eye. This is where you discover, service and predict their needs.

Too many businesses are only interested in touching themselves under the counter.

My previous post – Commercial Quality Apple & Cinnamon Melomel – covered that ground. And for the life of me I don’t see how it serves the Tasmanian economy to lock my business venture out based on those constraints. I either make high quality local product, or I don’t.

Licensing, in this instance, is an insurmountable barrier that prevents me from capitalising on my core capabilities and it prevents the Tasmanian economy from becoming that little more sustainable.

The MBA in my head has been scrumming around for ways to circumvent this limitation. It’s what MBAs are trained to do – add up the numbers, figure the value and profits of a business and circumvent apparently insurmountable barriers to getting our products to market. Refinements to the business plan:

• Option A: Pass the business plan and product to a third party who would employ me as a mead maker. They carry the business licensing, they deal with the business finances and risk. I work solely as an employee with no say in the direction of the business. Sadly, mead makers are probably as replacable as infrastructure.
• Option B: Pass the business plan and product to a third party and finance them to achieve these outcomes. However, the limitation as an investor would be that I don’t join the industry but remain on the financial side as a shadow interest. This would give me no input into controls for quality, branding or product evolution.
• Option C: Move away from the licensing restriction and produce the mead overseas. This would mean importing the Tasmanian honey into that country and it trades off against losing the Tasmanian hand-produced product branding advantage that I would be interested in pursuing. This would in turn influence my ability in several years to market the mead – melomels and cysers – into the growing middle class of Asia, particularly India and China.

While I can’t currently move forward as a mead producer it suits me fine to continue experimentation and product evolution. However, as my issue now is replication of the product we are coming to the stage of choices about those three options. Within 2 years I will be at the stage where biting at the bit is a standardised high quality low-volume production that could be expanded.

There are always ways around insurmountable business obstacles. Usually with trade-offs. And there are probably more ways to skin that cat than Options A-C.

It would be nice in 5 years to be producing commercial quantities of exportable product from a Tasmanian property. But that’s probably a dream. And it’s a dream that would take a lot of external financing.

She wrote:

I wanted to let you know that your Apple & Cinnamon is amongst the best mead I’ve ever tried. I knew it would be nice when I took the cap off, the bouquet was magnificent; I have been in heaven having a sneaky little glass (or four) every night. Honestly, I have a friend who makes mead for a living and he would be proud to produce something like that.

So here I am with an MBA and the ability to produce a fine quality Tasmanian gourmet product at around the $30 price point. I would spend another year perfecting this particular melomel, riding on the back of local vineyards educating the visitor’s palate, and securing consistency of produce in the supply chain to follow through over the next few years with orange melomel, cyser and plain mead. The step to high volume production potential is in mixing a consistent plain mead and fruit juice blend marketed in highly differentiated frosted glass bottles available in four packs or as singles.

However, the Tasmanian government know this scenario could never be the case. I’m unable to be licensed to manufacture or sell fermented products. I’m unable to be a person of influence within an organisation that manufactures or sells fermented products. It’s the same legal barrier that prevents me managing a hotel or running a casino or being a bookie.

Meanwhile, the Tasmanian economy heads down the shitter because Rome burning hasn’t reached the common sense of the populace that there should not be one single local university graduate out of work. We don’t need a government that researches economic development – we need a government that creates an environment where we can do business. We don’t need a government that is one quarter of our State’s labour force. We need a lean, economically vibrant, entrepreneurial, supportive government that cares about small to medium enterprises with the vigour it used to reserve for certain large industry cohorts.

I mean, for Heaven’s sake, don’t Tasmanian politicians see the potential of a burgeoning middle class through India and China? Don’t they realise the small speck of that market that could sustain the Tasmanian economy over the long haul between now and 2030? There are people across the world rethinking their allegiance to the Walmarts and IKEAs. They are cashed up and demand quality products that are unique, hand crafted and have an exotic Tasmanian provenance.

If we can just stop looking inward for a moment we can dig our way out of this pile of crap economic situation. We’ve got the tools AND the talent. We just need the will to enable entrepreneurship and stop locking people like me out.

[End rant... 20:47 time for an imported coffee]

A Company is Legally a Person, but…

Before anybody sends me a factional ball-busting via my email address let me put you straight on one point. Business… is not… about… your politics.

Maybe you didn’t hear me so I’ll go to some length to explain that a company is a legal person in its own right. It’s a person without a vote. But it’s a person who can exchange goods and services for money; it can be stolen from and it can steal from others; it pays tax. A company can be ethical or unethical depending on the type of business and the people who engage it. But a company is still only a business. It’s not a real person; a company is a legally recognised pseudo-person created for business transactions.

This should give you a clue as to why personal politics doesn’t belong on that company car. The business isn’t the owner. Not legally. Not actually. And definitely not in the voting context. Even if their business isn’t a company, if they are a sole trader or a partnership, it still doesn’t make sense. It’s kind of (mostly) dumb.

The Marketing Message is Off Message

Now step back a moment and think about the business marketing message a few million Australian Labor Party voters take away from the political statement on that company car. Aside from the fact the business owner could be an aggressive political stooge with an agenda other than serving customer needs.

It translates as… “Labor voters are stupid”… “Labor voters are not welcome”… “We reserve the right to treat anybody who doesn’t agree with our political opinion as a lesser customer.” The message is OFF MESSAGE. The message is “Our brand is political. Our brand takes sides.” If our brand happens to sell pens, matresses, accounting services or dildos I can just about tell you for a fact that a brand shouldn’t take sides. Not in an election. Not on a hot topic like human induced global warming and carbon pricing. Not when it’s easier to serve both opinions in that debate equally for maximised profit.

Taking sides is just plain redneck dumb, unless they sell mining equipment or something justifiable to the long-term marketing strategy.

A brand shouldn’t be about giving potential customer’s a quick punch in the face in the carpark. Unless, as mentioned, they sell mining equipment to Gina Rinehart.

Businesses don’t Vote

My point is that when a business owner sticks political messages to their company car it goes beyond a personal statement and becomes the marketing message of the branded business. Because brand is the perception in the mind of the market and that sticker affects that perception. Just like the way the business owner dresses for success instead of trotting out in flip-flops. Just like they don’t kick a stray animal. Just like anything else they do as a person in reference to being that business reflects back onto the business brand – the perception in the market – with a laser light of intense scrutiny.

Were I employed as their business consultant the first thing I would do would be to walk down to that car and remove the sticker.

Businesses don’t vote.

But it’s not as easy as poking your head in their front door and saying “Hey, you could be $50K better off at the end of this year if you do X and Y.” Their response would more often than not be a barrier that would preclude any chance of further conversation.

“Get the fuck out of my business!”

So they lumber on doing what they do well enough to stay in business. The ‘bad egg’ keeps disaffecting morale. Money that should be in the account remains unpaid, or is tied up in assets that really should be leased. They simply don’t know something is broken.

Nearly every time, it turns out the problem is deeper – they don’t have a business plan or an integrated marketing strategy. And if they do, it’s very rare that small business have considered keeping those as live documents that can be used to out-compete competitors.

Or they mistakenly imagine everybody doing roughly the same thing in the market are their direct competitors.

Most of those small businesses haven’t had the time or inclination to investigate the Competition and Consumer Act 2010, formerly the Trade Practices Act 1974. Just walk around your CBD shopping environment and look at all those “NO REFUND” signs.

This is where I push forward an unwanted piece of wisdom. Small businesses should consider paying somebody, or a team, to manage and grow their business with a strategic focus. Hire some decent management. Simple. Hire people that understand human resource management, organisational culture, how to author and maintain and implement strategies in the market. Hire people who know the legal and ethical responsibilities. Someone who understands the cost of capital and time value of money in decision making.

Just like that same small business might be smart enough to pay an accountant or a solicitor when the need arises.

Why? Because a professional should make a business far more money than they ever cost. And, at the same time, the business owner is freed from the time-consuming soul destroying tasks they were never trained to undertake.

Quite often I find myself walking out of these small businesses and scratching my head as to whether they’ll be operating in 2-5 years. I can’t help it. But if they don’t know anything is broken they’re not going to want to hear how to fix it. We had a roofing tradesman here last year who I could almost guarantee is rolling over a $100K short-term loan to cover his slack approach to collecting money due.

Now you know the challenge of being a business development management consultant. And what they do beyond the infamous management jargon.

The Problem with Pinterest is the Terms of Service

OK, before I get anymore troll action from Pinterest fan-girls who are upset that somebody isn’t impressed by the business model of their favourite new web-tinsel frivolity… let’s all just pull our heads in and look at this as grown-ups. It’s not about your jollies or the things you do with your web-besties when porn loses its lustre – this is about the law.

When you join and upload content to Pinterest you are legally entering an agreement that affects you (as an adult in the real world) and at least in that regard it should be hitting your radar. Because, love their service or not… the idiot that will be sitting in a courtroom is more likely you than representatives of Pinterest. It’s in their TOS… that TOS that pretty much throws you to the wolves.

Kalliopi Monoyios posted an article this week titled Pinterest’s Terms of Service, Word by Terrifying Word pointing out the magic words within their TOS that should get your adult brain firing. One paragraph from the Pinterest TOS reads:

By making available any Member Content through the Site, Application or Services, you hereby grant to Cold Brew Labs a worldwide, irrevocable, perpetual, non-exclusive, transferable, royalty-free license, with the right to sublicense, to use, copy, adapt, modify, distribute, license, sell, transfer, publicly display, publicly perform, transmit, stream, broadcast, access, view, and otherwise exploit such Member Content only on, through or by means of the Site, Application or Services.

Kalliopi points out the bits you need to be concerned about… “worldwide, irrevocable, perpetual, non-exclusive, transferable, royalty-free license, with the right to sublicense… yada yada. Yes, pretty much all of it.

In simple terms you hand over the content you uploaded to your Pinterest account… it goes to Cold Brew Labs forever and you can’t change your mind and they can on-sell, repurpose or do whatever the hell they want to squeeze a quid of profit from it anytime they consider it worthwhile. You have given away your stuff.

Pinterest’s Aggressive Opt-Out not Opt-In Feature

Oh yeah, it most likely wasn’t your stuff. Hey, it could even be my stuff or the stuff from somewhere bold enough to sue your sorry butt. It could belong to an aggressive company that protects its intangible business assets, like Getty Images. Or Associated Press. These are organisations that can and will pursue you to protect their profit margins.

Kalliopi hits it on the head when he points out that the real problem is Pinterest’s TOS “don’t mirror the intentions of users”.

Yes, Pinterest provides a snippet of code that will tell people (like they’ll listen) that you don’t want to share your online images in their service. However, as a web developer who just had to put that snippet onto my clients’ websites I don’t think it’s a good direction to head where one business model requires every website on the Internet to opt out of their environment. Here’s a better idea… ask us if we want to opt into the Pinterest service… let those websites willing to play in the little sandpit of their business model to put a piece of code into every clients website.

And you are the Sole Owner of all Member Content

Glendon Mellow brings out the most salient point in my concern about the Pinterest TOS… ownership. It reads that you:

“…are the sole and exclusive owner of all Member Content…”

and you,

“agree not to do any of the following: Post, upload, publish, submit, provide access to or transmit any Content that: (i) infringes, misappropriates or violates a third party’s patent, copyright, trademark, trade secret, moral rights or other intellectual property rights…”

That means the only person who will get into major legal shit is YOU, the customer. Why? Because when you upload your Pinterest content for sharing you are claiming you own the intellectual property rights of that content and you are passing total control over to Cold Brew Labs to do with that content whatever they wish. That means eventually somebody like Getty Images… or even me… will come back to haunt you.

Any content creator, commercial or non-commercial, needs to be concerned about this type of business activity affecting their work and legal environment.

My point to Pinterest users is that they stand a very good chance of losing a court case if they give away the wrong person / company’s intellectual property to Cold Brew Labs. Depending on the country that intellectual property crime occurs in, they could be pursued with extreme prejudice. Pinterest got them to agree to that from the beginning.

Don’t Say you weren’t Told about the TOS

No, I’m not against social web applications and all the better if they make some money. But I am against business models that are purposefully worded to capitalise on property theft while getting their users to foot the legal payload.

And I am against the idea that every website has to place explicit code asking to opt-out of the Pinterest service. What if twenty or a hundred web services adopted that arrogant attitude? Would we have massive web page headers loaded down with a thousand explicit meta tags to opt-out of each and every one? Features like that need to be opt-in or not at all.

And on that point alone the web industry bodies should be up in arms at the management team at Pinterest.

A bad exploitative business model is just that. As long as Pinterest keep that wording in the TOS there will be an issue to answer. So go play on Pinterest until your bum falls asleep on your office chair for all I care, but don’t dare suggest (on Twitter or elsewhere) that this is an ethical manner of doing business. It isn’t. That TOS really isn’t.

Here’s a passing tip: Don’t sign dumb legal contracts on the Internet and expect that life will treat you fairly. The old saying, now almost a cliche, applies… “if you’re not paying for the product then you are the product.” Pinterest is no different.

Time Periods to Reach a Target Sum (Single Amount)

Given a need to determine how many years it would take for a $10,000 investment at 7 per cent to grow to $16,000 we could treat n as the number of years and i as the interest rate.

The first step is to divide the first payment (Present Value) by the amount received at the end (Future Value):

$10,000 / $16,000 = 0.6250

The second step is to place that value into the Present Value Interest Factor:

Present Value Interest Factor_0.07,n = 0.6250

The final step is to look in the Present Value Interest Factor (for a single amount) Time Value of Money Chart in the column for 7 per cent. Our number (0.6250) falls just short of 7 years with 0.623. Therefore, an initial deposit of $10,000 at 7 per cent will take nearly 7 years to mature into $16,000.

Time Periods to Reach a Target Sum (Annuities)

In a similar fashion it is possible to calculate the unknown term of an annuity. In this case we might want to work out how long it would take to repay a $16,000 loan at 7 per cent with equal end of year payments of $3,000.

The first step is to divide the size of the loan by the size of the payments:

$16,000 / $3,000 = 5.3333

The second step is to place that value into the Present Value Interest Factor of an Ordinary Annuity:

Present Value Interest Factor of an Ordinary Annuity_0.07,n = 5.3333

The final step is to look in the Present Value Interest Factor for an Ordinary Annuity Time Value of Money Chart in the column for 7 per cent. Our number (5.3333) is just short of the number corresponding in that chart for 7 years (0.5.389). Therefore, our loan of $16,000 at 7 per cent with payments of $3,000 will take just under 7 years to complete.

Growth Rate (Single Amount)

A similar problem is working out the growth rate, or the compound annual interest rate, across a number of cash flows. The example we will use is:

• 2011 – $18,935
• 2010 – $18,154
• 2009 – $17,406
• 2008 – $16,688
• 2007 – $16,000

Note that there are five cash flow payments and we are interested in the four growth rate spaces (represented in calculations as i) that fall between them.

The first step is to divide the earliest payment (Present Value) by the latest payment (Future Value):

$16,000 / $18,935 = 0.845

The second step is to place that value into the Present Value Interest Factor:

Present Value Interest Factor_i,4 = 0.845

The final step is to look in the Present Value Interest Factor (for a single amount) Time Value of Money Chart in the row for four years. Our number (0.845) falls closest to the value for 4 per cent (0.855). Therefore, five annual payments with equal growth from $16,000 to $18,935 would have a growth rate just over 4 per cent.

Growth Rate (Annuities)

We can also work out the interest rate on an annuity. For example, if we took out a business loan of $16,000 with equal end of year repayments of $4,300 over the next four years we could work out the effective (after compounding) interest rate:

The first step is to divide the size of the loan by the size of the payment:

$16,000 / $4,300 = 3.7209

The second step is to place that figure into the Present Value Interest Factor of an Ordinary Annuity:

Present Value Interest Factor of an Ordinary Annuity_i,4 = 3.7209

The final step is to look in the Present Value Interest Factor for an Ordinary Annuity Time Value of Money Chart in the row for four years. Our number (3.7209) falls closest to the value for 3 per cent (3.717). Therefore, a loan of $16,000 with four equal payments of $4,300 over four years has a growth rate of around 3 per cent.

Conclusion: The Idea of Time Value of Money

One of the most important things to understand about administering your business is that money has a time value. The longer money pools in your account and the more effectively it is utilised in that process the better it will always be for your business. General rules like pay your bills at the end of the invoice period and collect as early as possible are healthy ways to operate.

But, even more important, I hope this short series on Time Value of Money 101 has given you some basic formulas that can improve your business decision making. None of this is rocket science, but if you expect to compete in the hyper-competitive modern business environment over the long-term it’s exactly the sort of skill you need to be bringing on board.

While money isn’t the reason you should be in business… it should be to serve a public need not met by government and a by-product of doing that well means people will give you money… the simple fact is that money is the blood of any business. If you can’t meet your current liabilities (short-term debt) as they fall due then profitability means squat, you’re done. It’s over.

If you really want to do well in business you’ll try to learn everything about money that you can get your hands on… and then some. Enjoy.

Time Value of Money 101 Series

1. Time Value of Money 101: Present & Future
2. Time Value of Money 101: Financial Tables
3. Time Value of Money 101: Ordinary Annuities
4. Time Value of Money 101: Annuities Due
5. Time Value of Money 101: Mixed Streams
6. Time Value of Money 101: Compound Interest (redux)
7. Time Value of Money 101: Nominal versus Effective Interest Rates
8. Time Value of Money 101: Deposits to Reach a Target Sum & Loan Amortisation
9. Time Value of Money 101: Time Periods to Reach a Sum & Growth Rates

Deposits to Reach a Target Sum

If we had to work out the size of deposits needed to reach a target sum of $50,000 at 4 years with 6 per cent interest we can revisit the Future Value of an Ordinary Annuity (with the help of Time Value of Money Financial Tables) where PMT is the size of the periodic payments, i represents the interest rate and n is the number of years:

Future Value of an Ordinary Annuity_n = PMT * (FVIFA_i,n)

Shuffling this formula around gives us another formula to discover the size of payments given the same information:

PMT = Future Value of an Ordinary Annuity_n / FVIFA_i,n

This becomes:

• PMT = Future Value of an Ordinary Annuity₄ / FVIFA_0.06,4
• PMT = $50,000 / 4.375
• PMT = $11,428.57

This means that four payments of $11,428.57 at the end of each year at 6 per cent interest will result in the target sum of $50,000 in the account.

Loan Amortisation

Amortisation means to pay off or to decrease over a period. So loan amortisation is the paying off of a loan at a given percent interest rate over a set period of time with equal payments being made at the end of each year.

If we take out a loan of $30,000 at 9 per cent interest over 5 years we can revisit the Present Value of an Ordinary Annuity:

Present Value of an Ordinary Annuity_n = PMT * (PVIFA_i,n)

Shuffling this formula around we can once again identify for the size of payments:

PMT = Present Value of an Ordinary Annuity_n / PVIFA_i,n

The formula works through as:

• PMT = Present Value of an Ordinary Annuity₅ / PVIFA_0.09,5
• PMT = $30,000 / 3.890
• PMT = $7,712.08

This means that five annual payments of $7,712.08 at the end of each year at 9 per cent interest will pay off the $30,000 loan.

If you are a little confused about the two concepts then consider that a deposit to reach a target future sum is solved for a Future Value because the sum itself is in the future. Whereas, a loan is taken out in the present and needs to be solved for a Present Value as it is paid off over time (amortised).

A Loan Amortisation Schedule

When you take out a loan the bank will create an Amortisation Schedule that explains the breakdown of principal and interest as it is paid off over the term of the loan.

The Next Step: Calculate the Number of Time Periods

Calculating the deposits needed to accrue a future target sum and working out loan amortisation are handy skills for business managers. In the next article we will look at the last Time Value of Money application to be discussed in this short series – using Financial Tables to calculate the number of time periods to reach a specified future sum.

I would also advise you to pick up any decent copy of a managerial finance textbook to underpin these articles and to complete the exercises that will cement this understanding at the end of each chapter. The textbook will also provide more precise context important to your understanding.

Time Value of Money 101 Series

1. Time Value of Money 101: Present & Future
2. Time Value of Money 101: Financial Tables
3. Time Value of Money 101: Ordinary Annuities
4. Time Value of Money 101: Annuities Due
5. Time Value of Money 101: Mixed Streams
6. Time Value of Money 101: Compound Interest (redux)
7. Time Value of Money 101: Nominal versus Effective Interest Rates
8. Time Value of Money 101: Accumulation of a Target Sum & Loan Amortisation
9. Time Value of Money 101: Time Periods to Reach a Sum & Growth Rates

Nominal & Effective Rates of Interest

It is important to be able to differentiate between the interest that you sign up for in a contract and the amount of interest that actually accrues in the account.

The Nominal Interest Rate (NIR) is the interest rate stated in the contract. While, the Effective Interest Rate (EIR) is the rate of interest that is paid or accrues and this takes into account the effect of interest compounding over time. If compounding of interest is annual then the NIR and the EIR will be the same.

Calculating the Effective Interest Rate

The formula to calculate the EAR, where i represents the NIR and m represents the compounding frequency:

EAR = (1 + (i / m))^m – 1

For a NIR of 12 per cent we can look at the calculations for annual and quarterly EIR:

• Effective Interest Rate = (1 + (0.12 / 1))¹ – 1
• Effective Interest Rate = 1.12 – 1
• Effective Interest Rate = 0.12

This demonstrates that the EIR of 12 per cent does equal the NIR of 12 per cent when compounding annually. However, this is not the case for quarterly compounding (or any compounding shorter than a year):

• Effective Interest Rate = (1 + (0.12 / 4))⁴ – 1
• Effective Interest Rate = (1.03)⁴ – 1
• Effective Interest Rate = 1.1255 – 1
• Effective Interest Rate = 0.1255

Quarterly compounding produces an EIR of 12.55 per cent from a NIR of 12 per cent. The shorter the compounding period the larger the EIR becomes.

The Next Step: More Applications of Time Value of Money

The difference between NIR and EIR is one of those small but fundamental pieces of knowledge that you need to make effective financial decisions. In the next article we will look at other applications of the Time Value of Money.

I would also advise you to pick up any decent copy of a managerial finance textbook to underpin these articles and to complete the exercises that will cement this understanding at the end of each chapter. The textbook will also provide more precise context important to your understanding.

Time Value of Money 101 Series

1. Time Value of Money 101: Present & Future
2. Time Value of Money 101: Financial Tables
3. Time Value of Money 101: Ordinary Annuities
4. Time Value of Money 101: Annuities Due
5. Time Value of Money 101: Mixed Streams
6. Time Value of Money 101: Compound Interest (redux)
7. Time Value of Money 101: Nominal versus Effective Interest Rates
8. Time Value of Money 101: Accumulation of a Target Sum & Loan Amortisation
9. Time Value of Money 101: Time Periods to Reach a Sum & Growth Rates

Semi-Annual and Quarterly Compounding

You will find that interest is going to be compounded by financial institutions in all sorts of increments – annually, monthly, weekly or even daily. So we need a fast and effective formula to calculate the effect of that compounding; where i is the interest rate, m is the number of terms in the year and n indicates the number of years:

Future Value_n = Present Value * (1 + (i / m))^m*n

Solving for a quarterly compounding of $2,000 at an interest rate of 8 per cent over 2 years:

• Future Value₂ = $2,000 * (1 + (0.08 / 4))^{4 * 2}
• Future Value₂ = $2,000 * (1 + 0.02)⁸
• Future Value₂ = $2,000 * (1.02)⁸
• Future Value₂ = $2,000 * 1.1717
• Future Value₂ = $2,343.40

Skinning the Future Value Cat another way

The example I chose was specifically taken to show the relationship between the Future Value result of compounding over those eight time periods ($2,343,40) with the equivalent result provided by the Financial Tables for Future Value of a fixed amount ($2,332).

• Future Value = PMT * FVIV_i,n
• Future Value = $2,000 * FVIV_0.08,2
• Future Value = $2,000 * 1.166
• Future Value = $2,332

Had the interest rate been 7 per cent and the quarterly interest over 3 years this would have been more difficult to prove on the Financial Tables because the term for each period’s interest rate would have reduced to 0.0175 per cent across 12 compounding periods. Understanding this relationship, it would be advisable to stick with the formula created specifically to calculate compound interest more frequently than a year.

Continuous Compounding

Continuous compounding is where interest is immediately and continuously earned and compounds interest on itself. The compounding periods become extremely small. This is the highest rate of interest that can be earned as compound interest.

To calculate a continuous compounding of interest the Future Value Interest Factor formula becomes:

FVIF_i,n = e^i*n

This alters the formula for calculating the Future Value and e can be taken as 2.7183:

Future Value_n(continuous compounding) = Present Value * (2.7183^i*n)

To follow this continuous compounding calculation through with $2,000 at 8 per cent over 2 years:

• Future Value_n = $2,000 * (e^i*n)
• Future Value₂ = $2,000 * (2.7183^0.08*2)
• Future Value₂ = $2,000 * (2.7183¹⁶⁾
• Future Value₂ = 2,347.02

The Next Step: Nominal & Effective Rates of Interest

In the next Time Value of Money article we will discuss the difference between nominal and effective annual rates of interest.

I would also advise you to pick up any decent copy of a managerial finance textbook to underpin these articles and to complete the exercises that will cement this understanding at the end of each chapter. The textbook will also provide more precise context important to your understanding.

Time Value of Money 101 Series

1. Time Value of Money 101: Present & Future
2. Time Value of Money 101: Financial Tables
3. Time Value of Money 101: Ordinary Annuities
4. Time Value of Money 101: Annuities Due
5. Time Value of Money 101: Mixed Streams
6. Time Value of Money 101: Compound Interest (redux)
7. Time Value of Money 101: Nominal versus Effective Interest Rates
8. Time Value of Money 101: Accumulation of a Target Sum & Loan Amortisation
9. Time Value of Money 101: Time Periods to Reach a Sum & Growth Rates