The Time Value of Money

I visited the grade 9 business class for our second lesson. I chose to focus on the time value of money. It’s a pretty simple concept. Would you rather have $1.00 today, or $1.00 next month? Most people will answer “today.” What if I offer you $1.00 today or $2.00 next month? The class was split on that question. My guess is that the amount was too small ($1.00 to wait 30 days) to sway some of the students. But it teaches that the time value of money is subjective and isn’t equivalent for everyone.

Financial planning has been described as “a bunch of formulas”. It seems a little dismissive, but it may also overstate the complexity. Most of financial planning can be summed up as the (judicious) use of the time value of money (TMV) calculation. I presented it to the students as Future Value = F( Rate, Number of PERiods, PayMenT, Present Value). In English, the future value can be calculated as a function of the interest rate, the amount of time, the payments (in or out) and the present value. In Excel (or other spreadsheet, I like LibreOffice), we can use the =FV() function to find out how investments or debt will grow over time.

Here are the two practice questions I gave the students. They seemed obvious to me, but I’m very familiar with this calculation. 1. If you start at age 25 with $0, earning 7% per year, how much do you have to save each year to earn $1 million by age 55? In this case, we are looking for the payment, how much we need to save. That means we need to use =PMT() in Excel (which is why I used the funny capitalization above). Simply enter the rate, years, starting amount and ending amount like this: =PMT(7%, 30, 0, $1000000) and press enter. Try it, and find out how much you’d need to save per year. I’ll give the answer at the end.

2. If your aunt gives you $5,000 at age 18, and you invest it at 10% guaranteed (however unlikely), how much will you have by age 65? We’re trying to find the future value, so we’ll use =FV(). This is a little trickier because it’s missing a piece of information: how much is the payment? Not adding to the account means the payment is $0. Try to figure this one out in Excel before I give you the formula. When you see the answer, you’ll see why I’ve been tempted to do this for my kids and nieces and nephews. =FV(10%, 47, 0, 5000) If the answer comes out negative, that’s normal and you can ignore it (or use -5000 for the present value).

The next three questions are related. 1. If you save $200 a month, what rate do you need to earn to save up $5,000 after 24 months for a vacation? The tricky part here is that the payment is given per month, so the result will be an interest rate that’s also per month. =Rate(24,-200,0,5000)*12 I multiply by 12 to get the annual rate. The answer is 4.24%. Note that if a person saves $200 per month for 24 months, they’ve saved $4800. If they earn 4.24%, they can spend $5,000 cash on their vacation.

2. If you pay off a $5,000 vacation over 24 months at 7%, how much did you pay in total? Again, the payments are made monthly, so we need to adjust the interest rate to monthly (7%/12) and find the payments, then multiply by 24 to find the total amount. =PMT(7%/12,24,5000,0)*24 Notice that we started with $5000 and paid it down to 0$. The total amount paid was $5,372.71, much more costly than paying cash.

3. If you pay $5,000 for a vacation on your credit card, at 18% interest, and pay $127 per month, how long will it take to pay it off? Try to figure this one out in Excel before I give you the answer. We’re looking for the length of time, so you’ll use =NPER(). The answer should be 59.97 months (or six years). If you pay $127/mo for 6 years, it cost you $7,616.82. That’s why not paying off your credit card can result in spending 50% more for your purchases. (N.B. technically, credit card interest doesn’t compound this way, but the lesson is valid.)

I also prepared two final questions, but you can see why we ran out of time. 1. If a car costs $25,000, how much more do you pay if your loan is at 5% instead of 3% over 5 years? =PMT(5%/12,5*12,25000,0)*60-PMT(3%/12,5*12,25000,0)*60 or $1,353.81. 2. If a car costs $25,000, how much more do you pay if your loan is 6 years instead of 3 years at 3%? =PMT(3%/12,6*12,25000,0)*72-PMT(3%/12,3*12,25000,0)*36 or $1,175.53. As you can see, it makes a big difference to negotiate a lower interest rate and to afford a shorter repayment. (I buy used and pay cash.)

I hope you enjoyed lesson two. Have you used this type of calculation before to plan your financial future, investments or mortgage? If you enter your current savings and investments (PV), your savings goal (FV), your current savings amount (PMT) and your recent investment (or savings account) returns, how long until you can retire?

3 thoughts on “The Time Value of Money”

  1. I didn’t discover all this until I got to college and took a class on it (and how to use my Texas Instruments financial calculator). It changed my life. I couldn’t even pay attention to the lecture because I was just sitting in the back figuring out answers to my own questions: how long will it take for me to save for a car, how much money will my savings be worth in 5 or 10 years, How much do I have to save per month to hit a specific target by a certain date. I was hooked.

    Probably had a lot to do with my decision to become a CPA.

  2. Using the example of getting a million dollars always sticks with kids. I still remember the question of if you would rather have $1000 today or a penny today, two cents tomorrow, four cents the next day, etc for one month. The second option gives you something like 2.4 million dollars. I learned that question in grade 2. Your students are sure to remember your lesson for a while.

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