What is the correct answer for percent change when the start amount is zero dollars $0?
"There is no numerical convention in finance that I have ever seen.  If you look at statements or reports that measure growth when the starting value is negative or zero, you typically see ""n/a"" or ""-"" or ""*"" as the result.  Any numerical result would be meaningless.  Suppose you used 100% and another company had a legitimate 150% gain - where would the 100% change rank? What do my manager and investors expect to see? As a financial analyst - I would not want to see 100%.  I would instead rather see something that indicates that the % change is meaningless.   As an example, here's the WSJ documentation on change in Net Income: Net Income percent change is the change from the same period from a year ago. Percent change is not provided if either the latest period or the year-ago period contains a net loss.  Thinking about it in another context: Yesterday you and your friend had no apples. Today you have 1 and your friend has 20.  What percentage increase did you both have? Did you both have a 100% increase? How can you indicate that your friend had a larger ""increase""? In that case (and in finance), the context needs to turn from a percentage increase to an absolute increase.  A percentage increase is that scenario is meaningless." A value of zero or a negative value makes the percent change meaningless. Saying 100% when going from 0 to some other value is simply wrong. I have seen a similar situation several times when looking at a public company with a loss last quarter. On Google Finance or some other service, the PE ratio will be blank, N/A, or something like that. If the company does not currently have earnings, then the PE ratio is meaningless. Likewise, if the company previously did not have earnings, then the percent change of the earnings is meaningless. Also consider the example where the previous value was negative. If the previous value was negative 1 and the current value is positive 99, then this happens: A negative change? But the value went up! Obviously that value does not make sense and should not be shown. "I'd personally display ""n/a"" The only other answer that makes sense to me other is ""infinity"" (phone keyboard doesn't allow me to input the symbol). This would at least allow you to show direction by using positive and negative  infinity and mathematical as the the initial value approaches zero the percentage change approaches infinity which is the closet you can get to a meaningful value" "In general, when dealing with quantities like net income that are not restricted to being positive, ""percentage change"" is a problematic measure. Even with small positive values it can be difficult to interpret. For example, compare these two companies: Company A:  Company B:  At a glance, I think most people would come away with the impression that both companies did badly in Y2, but A made a much stronger recovery. The difference between 99.7 and 99.9 looks unimportant compared to the difference between 100,000 and 40,000. But if we translate those to dollars: Company A: Y1 $100m, Y2 $0.1m, Y3 $100.1m Company B: Y1 $100m, Y2 $0.3m, Y3 $120.3m Company B has grown by a net of 20% over two years; Company A by only 1%. If you're lucky enough to know that income will always be positive after Y1 and won't drop too close to zero, then this doesn't matter very much and you can just look at year-on-year growth, leaving Y1 as undefined. If you don't have that guarantee, then you may do better to look for a different and more stable metric,  the other answers are correct: Y1 growth should be left blank. If you don't have that guarantee, then it might be time to look for a more robust measure, e.g. change in net income as a percentage of turnover or of company value." As has been said before, going from nothing to something is an infinite percent increase! It is not 100%. Maybe you had a dollar and now have $101 that is a 10000% increase! Quite remarkable. I often work with symmetrized percent changes like: spc = 100 * (y2-y1)/(0.5 * (y1+y2)) Where I compute the percent with respect to the average. First this is more stable as often measurements can have noise, the average is more reliable.  Second advantage is also that this is symmetric. So going from 95 to 105 is a 10 % increase while going from 105 to 95 a 10% decrease. Of course you need to explain what you show. "Anyone who has any business looking at growth numbers will know thay are meaningless in the first year,  So all they need to know is that it's the first year.    It's no different than the Billboard music charts' treatment of the ""last week's chart ranking"" and ""movement up/down"" columns.  It will help with visual layout if the figure used is about the same size as a percentage number.   ""New"" fits nicely." In computing, you'd generally return naa%, for 'not a number'. Could you not put '-%' to show there is no value at this point? Surely the people seeing this aren't idiots and understand the charge on 0 is 0? What is the probability of a real occasion (meaning not just an example) being exactly zero? Even if you have 0.1 you can still do the math. Also, it is kind of depending on the occasion. For example, you want to calculate the ROI of an investment for which you had zero capital and you made that investment with leverage, meaning you got a loan. In order to get that loan you should have provided a collateral, so in this case as a starting sum you use the collateral. In another example, say EAT it's difficult to have exactly zero. So, in most cases you won't have to deal with zero values, only positives and negatives. "There are some assumptions which can be made in terms of the flexibility you have - I will start with the least flexible assumption and then move to more flexible assumptions. If you must put down a number 1, your go-to for this(""Change the start period to 1""), is pretty good, and it's used frequently for other divide-by-zero calculations like kda in a video game. The problem I have with '1' is that it doesn't allow you to handle various scales.  Some problems are dealt with in thousands, some in fractions, and some in hundreds of millions. Therefore, you should change the start period to the smallest significantly measurable number you could reasonably have. Here, that would take your example 0 and 896 and give you an increase of 89,500%. It's not a great result, but it's the best you can hope for if you have to put down a number,  and it allows you to keep some of the ""meaning in the change."" If you absolutely must put something This is the assumption that most answers have taken - you can put down a symbol, a number with a notation, empty space, etc, but there is going to be a label somewhere called 'Growth' that will exist. I generally agree with what I've seen, particularly the answers from Benjamin Cuninghma and Nath. For the sake of preservation - those answers can be summarized as putting 'N/A' or '-', possibly with a footnote and asterisk. If you can avoid the measurement entirely The root of your question is ""What do my manager and investors expect to see?"" I think it's valuable to dig even further to ""What do my manager and investors really want to know?"". They want to know the state of their investment. Growth is often a good measurement of that state, but in cases where you are starting from zero or negative, it just doesn't tell you the right information. In these situations, you should avoid % growth, and instead talk in absolute terms which mention the time frame or starting state. For example:"
"When using Time Value of Money equations, you need to know when the flow starts. A mortgage for example, has a first payment at the end of the first time period, usually 1 month.  For savings, one can start the account with a deposit of course, or start by saying ""I will deposit $XXX at the end of each month.  The answer really depends on the exact details of the situation. In your example, I'm inclined to suggest first flow is 1 year out." I think is an excellent idea. Use free money or almost free to do a lump sump payment. My recommendation is to have a reminder to pay credit card before, almost finishing, the 0% APR period. I am sure everyone is different, but it has helped me a great deal. I have had several card balances go up and the interest on those per month was more than $200 in just interest combined.  I transferred the balances over to 0% for 15 months – with a fee, so the upfront cost was about $300. However, over the next 15 months at 0% I'm saving over $200 each month.  Now I have the money to pay everything off at 14 months. I will not be paying any interest after that, and I cut up all of my cards so I won't rack up the bills with interest on them anymore. Now, if I can't buy it with a debit card or cash, I don't get it.  My cards went up so high after remodeling a home so they were justified. It wasn't because I didn't pay attention to what I could afford.  My brother, on the other hand, has trouble using credit cards properly and this doesn't work for him. That's pretty typical for introductory problems.  It's leading you into an NPV question.  They're keeping the cash flows the same to illustrate the time value of money to show you that even though the free cash flow is the same in year 1 and year 4 or whatever when you discount it to present value today's stream is worth more than tomorrow's Assuming cell A1 contains the number of trades: will price up to A1=100 at 17 each, and the rest at 14 each. The key is the MAX and MIN. They keep an item from being counted twice. If X would end up negative, MAX(0,x) clamps it to 0. By extension, if X-100 would be negative, MAX(0, X-100) would be 0 -- ie: that number doesn't increase til X>100. When A1=99, MIN(a1,100) == 99, and MAX(0,a1-100) == 0. When A1=100, MIN(a1,100) == 100, and MAX(0,a1-100) == 0. When A1=101, MIN(a1,100) == 100, and MAX(0,a1-100) == 1. Of course, if the 100th item should be $14, then change the 100s to 99s. It helps to put the numbers in terms of an asset. Say a bottle of wine costs 10 dollars, but the price rises to 20 dollars a year later. The price has risen 100%, and your dollars have lost value. Whereas your ten used to be worth 100% of the price of bottle of wine, they now are worth 50% of the risen price of a bottle of wine so they've lost around 50% of their value. Divide the old price by the new inflated price to measure proportionally how much the old price is of the new price. 10 divided by 20 is 1/2 or .50 or 50%. You can then subtract the old price from the new in proportional terms to find how much value you've lost. 1 minus 1/2 or 1.00 minus .50 or 100% minus 50%. Let's say the money-giver gets apples by you and he gives you money for them. The money you now have is worth to get apples. If the money now would change its value to negative, the roles would change opposites and you'd owe the money-giver (whom you already gave apples to) even more apples. That's simply insane. The worst money value can be is zero. That would have been a good idea.  They don't charge interest on a $0 balance, but if you payoff your account after the cycle date, there is a hidden balance and that balance will accrue interest. It is only a few cents a day.  I just don't think it is legal for them to refuse to provide you a payoff quote mid cycle. I'm almost certain. When I worked for Discover it was a key point in training to not give the wrong amount and to make sure to use the calculator in the system to quote a daily balance, how much it goes up per day, and how much they should send if they were mailing the payment, giving consideration for the time it takes to receive/process the payment. "Emotion aside, you can calculate the cost of the funds you have tied up at the bank.  If I can earn 5% in a CD, my ""free"" checking with minimum $5000 balance really costs me $250/yr. You have money tied up, I understand, but where would you place it otherwise, and at what return?  The subject of frequent trading even at zero cost is worth addressing, but not the real subject of your question. So, I'll leave it for elsewhere." "Some stocks do fall to zero. I don't have statistics handy, but I'd guess that a majority of all the companies ever started are now bankrupt and worth zero. Even if a company does not go bankrupt, there is no guarantee that it's value will increase forever, even in a general, overall sense. You might buy a stock when it is at or near its peak, and then it loses value and never regains it. Even if a stock will go back up, you can't know for certain that it will. Suppose you bought a stock for $10 and it's now at $5. If you sell, you lose half your money. But if you hold on, it MIGHT go back up and you make a profit. Or it might continue going down and you lose even more, perhaps your entire investment. A rational person might decide to sell now and cut his losses. Of course, I'm sure many investors have had the experience of selling a stock at a loss, and then seeing the price skyrocket. But there have also been plenty of investors who decided to hold on, only to lose more money. (Just a couple of weeks ago a stock I bought for $1.50 was selling for $14. I could have sold for like 900% profit. Instead I decided to hold on and see if it went yet higher. It's now at $2.50. Fortunately I only invested something like $800. If it goes to zero it will be annoying but not ruin me.) On a bigger scale, if you invest in a variety of stocks and hold on to them for a long period of time, the chance that you will lose money is small. The stock market as a whole has consistently gone up in the long term. But the chance is not zero. And a key phrase is ""in the long term"". If you need the money today, the fact that the market will probably go back up within a few months or a year or so may not help." &gt;I don't understand the logic of converting a cost of funds of 4% to a monthly % and then subtracting that number from an annual one (the 1.5%).  I know it was wrong, so how would you approach it?  &gt;Unfortunately without seeing the case I really can't help you...there was likely much you have left out from above.    All the relevant details I received for the case are here. What other info are you looking for? First of all any loan will have the last payment be slightly different than the rest. Even if the interest rate is zero it is hard to have a perfect monthly payment amount. By perfect I mean the amount of the loan divided by the number of months would be $ddd.cc0000...  When looking at the amortization table the last payment will either be slightly higher or lower to adjust for the rounding that was done. My suspicion is that the rounding would have resulted in a left over 12 cents. It is also possible that you are paying it off slightly early and the computer is simply taking the leftover amount an spreading it over the remaining period of the loan. You could be paying it early because for the main part of the loan was paid to a company that rounds all payments to the higher dollar, or has a minimum monthly payment amount. I looked at the company you mentioned in the question, and searched the site for an amortization tool. I found it, and used the pre-filled in example. https://www.edfinancial.com/amortizationschedule?pmts=120&intr=6.8&prin=25000 If that last payment is not adjusted the borrower will still owe $0.12. The fact it equals your situation is a coincidence. But is does show what can happen. "of course if you asked me to give you $24.4955 I can't. No, but if I asked you to give me $24.4955 and you gave me a piece of paper saying ""I O U $24.4955"", and then this happened repeatedly until I had collected 100 of these pieces of paper from you, then I could give them back to you in exchange for $2449.55 of currency. There's nothing magical about the fact that there doesn't happen to be a $0.001 coin in current circulation.  This question has some further information." Consider inflation. If you invest $10,000 today, you need to make a few hundred dollars interest just to make up for inflation - if there is 3% inflation then a change from $10,000 to $10,300 means you didn't actually make any money. I think examining the effects and potential implications of China's involvement with the stock market may be productive. Some interesting examples would be the failed market circuit breakers and the restrictions of short-selling in 2016.  Not sure that this would qualify as a real topic, but may give you food for thought.