Lesson 7 - MsArgos/RMI_2501_Fall_2026 GitHub Wiki
(i) Think carefully before answering this question on your own: 'When is it better for me to have something now versus later? Why?'
(ii) Now share outside the classroom, if possible, with these classmates or one of them what your response to questions (i) are. You will be working with these randomly assigned classmates during the entire workshop.
(iii) Review the instructions of this lesson plan (the theme for our upcoming workshop), and try your best to answer questions (i) now in strictly financial terms (using the right terminology) and justifying it through mathematical thinking supported by real numbers (show off to your classmates how well you can manipulate the variables of the discount rate equation under different scenarios before you settle on one financial decision/plan).
(iv) State your name and share briefly what you have learned from following the steps above by answering questions like 'Did your answers stay the same throughout the exercise? Yes, no, why?'; 'Who did you actively approach to work together on this learning? How did this person(s) help you, or not?' 'Has your perception of math changed after this exercise? Yes, no, what, why, how?'
Disclaimer: Claude helped me convey my ideas for this scaffolded lesson plan more clearly and concisely; however, the ideas themselves, their progression and their scale are entirely my own.
PS. I highly recommend not to use AI in any of the learning steps above. It is completely fine if you struggle -- this is a sign that you are putting effort to grasp insights that are more likely to last through application and further manipulation. Share where you got stuck with your classmates and bring them to class.
Group1
Yitong: I think it is better to have something now when I need it immediately or when I can use it to create more value. But waiting may be better if I can receive more in the future. My decision depends on how valuable the future benefit is compared with having it now. After reviewing the lesson plan, especially the lottery example in step8, I understood the idea more clearly. A lottery winner may choose between $500000 today and 1000000 paid on annual installments over 20 years. At first 1000000 sounds better because it is a much larger amount. But the money is received over a long period of time. The later payments are not worth the same as the money we can receive and use today. The discount rate can helps we compare those future payments with money today by converting them into present value. I also think breaking down the formula is important. Instead of just putting numbers into it, looking at PV, FV, r, and t separately helped me understand what each part actually means and how they affect the decision. For example If FV stays the same, when r increases, PV decreases. But if PV stays the same, a higher r or a longer t makes FV increase. I also emailed my group members and shared my thoughts with them. My answer did not completely change, but now I understand the question more clearly from a financial perspective. I also realized that breaking a formula into smaller parts makes math easier for me to understand.
Ishaan: I would have to agree with Yitong here because I believe that it is better to have money today rather than in the future because of its earning potential, protection against inflation, and the lack of risk tomorrow. When you have money on hand, you can make it work immediately by investing it somewhere that earns interest. If you wait, your money begins to lose its value. For example, if you take $100 today and put it in a savings account with a 5% interest rate, it grows to $105 in one year; waiting for that exact $100 means you actively lose out on that extra $5. It becomes better to wait if you are offered a premium high enough to beat what you have on your own, like earning $110 next year instead of $100 today.
Misaki: I agree with Yitong and Ishaan. I prefer to have something now. At first, I thought it was better for me to have something later because it made me feel easier to make financial plan and it would be stable. For example, if you made sure when you could get money at a certain point in the future, you were able to manage plan expenses, such as rent, tuition, living expenses, and big purchase accordingly. Also, it may cause unexpected expenses more than you needed, if you had money now. However, you reasoned if timing and amount of receipt were determined, you could avoid impulsive spending and instead save or spend money in a planned way. Nevertheless, after read and think about financial perspective, I realized that there are cases in which receiving money now could be more valuable for ideas of discount rate and the number of time periods. You received money now, you could spend money or invest during time when you wait. Therefore, you need to think how you can use money if receive now and the value of money lost during that time rather just see amount of the money you receive in the future. For example, I considered the case where I could get $1000 now versus receive a larger amount five years from now. By using discount rate at 5% and a time of period is five years, you can calculate what that $1000 today would be worth in five years. FV=PV(1+r)^t FV=1000(1+0.05)⁵ FV=1000×1.2763=$1.276 This calculation shows if I received $1000 now and invest at 5% rate of return, it would grow about $1276 in five years. In other words, receiving $1276 now and receiving $1000 can be considered to have roughly the same value under given 5% rate of return. Before this calculation, I thought it was better to receive money if it was a larger amount simply. However, I realized that I received money now, I could use or increase money during waiting it through this review.
Kana: My initial answer to question (i) was that "it is better for me to have something now if it is necessary in that moment", which I agreed with my groupmates here. However, I was not considering the future value that I can grow from the present value. So, now that I have exchanged opinions with my groupmates and reviewed the lesson plan, my answer has been expanded to "it is better for me to have something now if it is necessary in the moment or I can grow its value towards the future more than what I can receive by waiting". Suppose I have a choice between receiving $90 now or $100 one year from now. If I receive the money now and put it into a savings account with 5% interest rate, the future value in one year would be calculated as 90(1+0.05)^1=94.5, meaning it would grow to $94.5 after a year. So, in this case, I can decide that it is better for me to wait one year and receive $100 one year from now. But what if the choice was to receive $95 instead of $90 now, and the interest rate of my savings account was 7% instead of 5%? If I receive the $95 now and put it into my savings account, the calculation would be 95(1+0.07)^1=101.65, meaning that after a year, the money will grow to $101.65. So in this case, I would take the $95 now over $100 one year from now. My general answer did stay the same throughout the exercise but I expanded it with another point as I realized I forgot to consider the value we can grow towards the future by hearing my groupmates' opinions and reading the lesson plan. I actively shared opinions with my groupmates through emails, which helped me develop my thoughts and understand this topic on a deeper level. My perception on math did not really change after this exercise because I have always enjoyed math since I was little until now, but I did find it fun and interesting how we can apply math to think about daily financial activities.
Gentoku: My first answer was that "it is better to have something now" because of the theoretical efficiency of getting money immediately. However, after reading others' opinions and reviewing the lesson plan, I realized that making this work in the real world requires many factors, such as the financial knowledge and capability to deal with concepts like interest and inflation. Suppose I have a choice regarding whether to receive 100,000 yen today ($PV = 100,000$) or in the future. If I receive it today and just hold onto it under an inflation scenario (assuming an inflation rate of approximately 2%), its real value falls. However, if I manipulate the variables by investing that 100,000 yen in a financial product yielding an annual interest rate of 5%, which exceeds the inflation rate. In that case, FV = 100,000 × (1 + 0.05)¹ = 105,000, meaning that after one year, it would be worth 105,000 yen. Conversely, if interest rates remain lower than the inflation rate, the theoretical advantage of receiving payments now diminishes. I understood that unless I simulate different scenarios using various values for variables and run it myself to compare and verify the result, I cannot develop a truly rational financial plan. My answer did not change, but it expands a lot as I learned how to apply mathematical formulas and financial concepts to real-world scenarios like Japan current economy. And it will definitely help me after I start my company. Through this exercise, I again realized that math and finance are powerful tools needed to protect and grow our assets in complex real-world situations, rather than just abstract calculations.
Group2 Mayuko: I think it is better for me to receive money later. Both options have pros and cons, but if I receive money right now, I will probably spend it quickly on things I want. I think I would use it to buy something or hang out with friends rather than invest in experiences. If I receive money later, I can plan how to use it for meaningful experiences, such as traveling. In the meantime, I can save money and prepare for experiences that require a lot of money. I might give in to my immediate desires, and I would probably spend the money on the coat I want the most right now. I tend to struggle with saving money. I know that I need to save money for traveling with my family or friends, but I often cannot do it after receiving money from my part-time job. I tend to spend as much as I earn, but this is a dangerous habit for my future, especially when I start working and need to pay for living expenses such as groceries, housing, and family-related expenses. However, according to the calculation, FV = PV (1 + r) ⁿ, the future value changes depending on the number of periods and the interest rate. As the number of periods increases, the future value also increases. The total is going to become $11.94.This is because, if I keep my money invested for a longer period, it has the potential to grow through compound interest, making the future value higher than the original value. To do so, if I get $10 right now, and the discount rate (r) is 3%, I will get the money six years later. If we calculate the future value, we can use the formula FV = 10(1 + 0.03)⁶. This amount is higher than the original value of $10, so we can clearly see that money can grow over time if we invest it at a 3% interest rate for six years. However, if we will receive the same amount of money in the future, it means that if the future value and present value are the same, there is no interest rate or discount rate. Therefore, we should receive the money as soon as possible.
Swara: I agree with what Mayuko has said. While on some levels or circumstances it can be/feel more beneficial to receive the money later rather than now, as in a practical sense, it can help to save and invest to grow the value. It makes more sense from a practical sense to avoid overspending and unnecessary expenses. However, looking at the money from a mathematical or economical point of view, receiving it now would be more "valuable". It is an understood concept that inflation is causing the value of the money to decrease over time, receiving money now would provide an opportunity to utilize a larger sum of money. For instance, if I am to choose in getting $1000 now or later (where later would be in 3 years), if I can acquire it now, and invest it with a 6% ROI (typical general ROI). Using the formula, FV = 1000(1+0.06)^3, which would provide a value of $1191. However, if want to receive the money after 3 years, with 3.4% inflation (in the US), the Present value would be PV = 1000/((1+0.034)^3). Which would be a value of $904.56, which suggests a significant decrease in the value you are actually receiving. Even if the inflation rate changes, a lesser value than the current $1000 can be expected. Hence, it can be understood that receiving money now is more financially beneficial. Nevertheless, learning and thinking more deeply has helped to explore how there can so many different situations where different steps are required. It kind of boils down to priority and needs to receive money now or later, which is something I did not think much about earlier.
Rin: At first, I think it is better to have something now when I need it immediately or can use it for something valuable. However, waiting can also make sense if I can receive a much larger amount later. My decision depends on the amount, waiting time, and what I could do with the money now. After thinking about this financially, I understood the time value of money. The equation is PV × (1 + r)^t = FV, or PV = FV ÷ (1 + r)^t. PV is present value, FV is future value, r is the discount rate, and t is the number of time periods. For example, if I could receive $500,000 today or $1,000,000 in 20 years, I can compare them using a 5% discount rate. In this case, $500,000 today has a higher present value. However, at a 3% discount rate, the present value is about $553,676, while at 8%, it is about $214,548. This shows that a higher discount rate decreases PV. Time also matters. At 5%, the present value of $1,000,000 is about $613,913 after 10 years, $376,889 after 20 years, and $231,377 after 30 years. Since t is an exponent, the effect of time is compounded. I also shared my thoughts with two group members. One focused on the practical side and said receiving money later could help prevent overspending and make saving for travel easier. The other focused on the financial side and said receiving money now could be valuable if it is invested and grows. Their different opinions helped me see that the answer depends on both personal priorities and financial factors. My answer did not completely change, but my reasoning became clearer. I learned that there is not always one simple answer because the discount rate, time period, investment opportunities, and personal priorities all matter. This exercise also changed how I see math. I realized that a formula is not just something to memorize. It can help explain real financial decisions and make them easier to understand.
Mayuko: Thank you so much, Swara and Rin. This is really helpful for my understanding. Even if I am scheduled to receive a large amount of money in the future, it may sometimes be better to receive the money now and invest it. By investing the money, I can earn more and potentially increase the amount beyond what I originally received. As a result, I will get more money in the future than the large amount I would have received later.
Group3 Amina: I think it is better for me to have something now when I need it immediately or when I use it to earn money, but receiving it later can be better if the future amount is big. Before this exercise, I mainly thought about the amount of money, but after learning about the discount rate, I realized that time also changes the value of money. For example, if I have 1000$ today or 1200$ in 2 years, with a discount rate of 5%, it would be PV= 1200/(1.05)^2= 1088.44. Since it is higher than 1000$ I would choose the 1200$ today. But if the discount rate was 10%, PV= 1200/(1.10)^2= 991.74$ so I would choose the 1000$ today. This showed me that the better choice depends on the discount rate and the number of time periods, and not just the amount of money. I also realized that receiving money now has an opportunity cost if I choose to wait. If I receive 1000$ I could invest it and earn a return while I am waiting. At the same time, waiting can be better if the future payment gives me a high enough return to compensate for the time I have to wait.
Dillon: While I do agree that the formulas mentioned in this section of our learning model are important as my partner demonstrated above, I think there are a significant number of variables missing that the equation simply doesn't account for when considering whether it is better to have something now or later. A compounding discount rate, that is to say a discount rate where the rate value is non-linear, is less than applicable in most real world contexts. In this equation, you are being given either the present value (PV) or the future value (FV) and asked to solve for the other when given a set rate of discount and the time by using either PV*(1+r)^t=FV or [FV/(1+r)^t]=PV. While Amina's example does a good job showing how the choice can be informed with only the information present in this formula, unless you go through every single independent line item and analyze its market trends and inflation or deflation and plan accordingly, this equation isn't that helpful. For example, if I was to have a television that I wanted to replace, but my current television still works, I should actually wait to buy the new television because they are on a trend downward in price and they will, if the trend is maintained, get more affordable the longer I wait for them. The same cannot be said for other things, especially those which are given any amount of government funding, especially in the U.S. Houses and land will always go up in value so, if I want to buy, the sooner the better, unless I have some information that the market is about to collapse or that there is about to be a bubble burst somewhere that will drastically impact the value of the market. In the real world, depreciation, inflation, and even interest rates are subject to variation that makes this equation nearly entirely unrealistic and non-functional for the purposes of many people's needs in Personal Finances.
Hitomi: I would have something now rather than later. Time value of money tells us that money we receive now is theoretically more valuable than receiving it later. For example, if I chose to receive $500 1 year later with a discount rate of 4%, by plugging the number into PV=FV/(1+r)^t, it would be PV=500/(1.04)=roughly 480. Given this, if I chose to receive the money 1 year later, the value would be smaller than the initial amount. On the other hand, if I chose to receive it right now, I would be able to invest it and expect to have more gain in the future. For example, by using FV=PV(1+r)^t, if I receive $500 right now and invest it with a 4% interest rate, in a year, I would receive FV=500(1+0.04)=$520. Therefore, considering the calculation result, having something now is preferable to me. Before doing this exercise, I thought having something now or later wouldn't make much difference because I don't have something I want right now. However, through the process of answering this question, such as looking back at time value of money or other terminology, I came to a conclusion that it is better to have something now because it broadens my financial options.
Group4
Carla: I think that receiving money now is a better solution, in my opinion. Suppose that I have the choice between receiving 1,000 euros now or 1,000 euros in one year. I would prefer to receive this amount today because I have the possibility to spend it directly or invest this money. However, after looking more closely at the exercise, I realized that the discount rate and time are two very important factors in the value of money, since they allow us to compare the value of a sum of money today with its value in the future. If we look at the formula: PV = FV/(1+r)^t, we can see that the higher the value of r, the lower the present value of a future sum, and when the value of t increases, PV also decreases. For example, if I can receive 1000 euros today or 1,200 euros in two years, with a discount rate of 5%, I can calculate the present value of the 1200 euros. 1200/(1+0.05)^2 = 1088.44 euros. Using this formula, I realize that I would prefer to wait because the value is higher. However, if the discount rate increases to 10%, the present value decreases and reaches 991.74 euros, so I would want 1000 euros immediately instead of waiting.
Therefore, my initial opinion has not really changed because if the two amounts are identical, I would still prefer to receive the money now. What has changed is mainly the way I think about this decision. I understood that we cannot simply say that receiving money now is always better. We also have to take into account the future amount, the discount rate, and time before making a financial decision. I also found that maths did change my perception on this exercice because the formula helped me understand real-life financial situations. Maths isn't something that we use to only study in class but we need it everyday, and I think that this formula is going to be useful in the future, especially when it comes to addressing our personal finances.
Sorana: In the first step of answering question (i), I have just written a table that line up situations. For example, I thought buying company's stocks which is new and having potential now is better than buy it later because their stock rate might grow and become more expensive. Another example is technology equipment. I thought I don't need to have brand-new technology equipment unless currently-using equipment is broken, because as the time pass, the quality of the equipment become better. The workshop gave me a chance to 'understand' the formula; PV = FV/(1+r)^t, especially in step 9. I have experienced installment loan last year to pay driving school tuition. I had to pay 320,000 yen for school, but I hadn't had enough money at that time. Therefore, I decided to divide into 12 installments although I need to pay interest. I paid 29,100 yen per a month for 12 months and its total cost was 349,200 yen. In the situation, I paid 29,200 yen more than the original tuition fee. I agree with Carla's idea that the value of money can change depending on when we receive or sped it.