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Financial Literacy #11: Intro to Investing

Now let’s get to the good stuff. We can get to the good stuff (making money with investments) because we’ve covered the bad stuff (paying money in interest.) If you avoid paying $20,000 in interest on your credit cards, you can invest that $20,000 and maybe turn it into $100,000. Remember: compound interest!

Here’s the key to investing. Look at the following sentence, read it a few times, and ponder it for a minute.

In general, the higher the risk you take in an investment, the higher your return will be.

Think for a minute, and then read on.

Ready? Does that make sense? Suppose you have $100, and a choice of only two places to put it. First, you can put it in a savings account. Or, you can invest it in the stock market.

The stock market investment is risky. When coronavirus hit, you would have lost 30% or so of your money. No one would ever invest in the stock market if the expected return wasn’t higher. So yes, the sentence above makes sense. Higher risk needs to come with higher return.

But wait … does that really make sense? The riskier investment has, well, risk! I just told you you would have lost 30% in early 2020! How can the return be higher?

The key is in those wiggle words I stuck at the beginning of the sentence: “In general.” The riskier investment might beat the less risky investment 75% of the time. Not every time, but most of the time. And on average, the riskier investment returns more.

Let’s take a look at some actual data. Here’s a spreadsheet; I hope you are able to click and download it:

Data-Lesson-11Download

That’s an Excel file. If you’re using Excel, just download it, find the file, and open it in Excel. If you’re using Google Sheets, download the spreadsheet open Google Sheets and click on the “file picker.” It looks like a folder on the right side of the screen:

This shows historical investment performance data from an NYU professor. I just included 4 assets:

  • The S&P 500 index. This is an index of 500 large stocks, so this is our proxy for investing in the stock market
  • 3-month T.Bill. T Bills are short-term bonds you buy from the United States Government. In other words, you loan the government money and they will pay you back in 3 months, with a little bit of interest. This is our proxy for cash. The government can print money, and so this is a really safe investment. A good savings or money market account should yield roughly the same rate.
  • Treasury Bonds. These are the same as Treasury Bills, except Treasury Bonds don’t return your money to you until 5 or 10 or 30 years later.
  • Baa corporate bonds. Baa makes it sounds like a sheep. But that’s a credit rating. Baa is pretty good, but not as good as, say Aaa. It’s kind of like school but with more grades. Here you are lending to a company, not the government. The risk of a company going out of business is still low, but not as low as the government going out of business. Higher risk leads to higher returns, long-term.

Don’t worry– you don’t need to understand all of this now. We’ll look at each of these in more detail in the next few lessons. For now I just want you to play with the risk and returns.

First let’s freeze the pane so the top labels (which investment) and the side labels (which year) always stay on the screen. Above I clicked on cell B6 and then clicked View–> Freeze Panes.

Now you can scroll to the bottom, to the most recent data. I held down the Control key (Command on a Mac) and pressed the down arrow. This will take you to the bottom of a column of data.

Then I used the average function and the stdev function. There’s something weird about my spreadsheet; when I tried to highlight only the cells in Column B, Excel highlighted everything in column B plus columns D, E, and F. That’s why I started with column D and copied backwards.

Average is of course the average of all of the data, and stdev is the standard deviation. We’re not going to get into too much of the math here. But the Standard Deviation is a measure of how much the numbers vary– how much they deviate from that average.

Roughly 68% of the values should fall within a range defined by the following 2 points:

The average PLUS the standard deviation

The average MINUS the standard deviation.

There’s a whole lot of assumptions you need to make for that 68% to be true. You can argue that the stock market return data is not what is called normally distributed; there tend to be more extreme years than you would expect from a normal distribution. But for our purposes, the standard deviation at least lets us see differences in the returns of the various asset classes.

Take a look at the data you calculated:

The average return of the stock market is 11.57% per year, with a standard deviation of 19.6% per year. So you would expect 68% of years to fall above a return of -8.01% but below a return of 31.16%.

It’s kind of crazy to think that nearly a third of the time, stocks will fall more than 8% or rise more than 31%. That’s some serious volatility!

Compare those numbers to the other investments. The other investments have lower average returns, but also lower volatility. Note that the higher the investment, the higher the volatility that comes with it. (Instead of using the word “volatility” here, I could easily use the word “risk” instead.) That’s not 100% true, since corporate bonds have a higher return and a slightly lower risk than the US Treasury Bonds. Still, higher returns generally come with higher risk.

Scroll back up the top and look at the S&P 500 returns from 1929-1932:

The sum will hopefully be displayed at the bottom of your screen. (If not, just use the SUM function.)The sum of those 4 years equals -85.90%! Now, you wouldn’t lose that much money; negative compounding works in yoru favor here. The second year you lose fewer dollars since you already lost some last year.

Let’s see what your actual loss was, assuming you started with $100 invested at the end of 1928. We’ll conveniently leave off the 43.81% return you would have gotten in 1928, and you’ll invest right at the start of the Great Depression:

Your $100 is now worth just $35.23. If you copy the formula down further, you will see that you get back to your original $100 4 years later. Still, when you invest you can’t see the future; sitting there with your $35.23 would be very painful! That’s the potential pain of higher risk.

Let’s do one last thing and see that $100 invested in all of these investments would have yielded over the entire period. get rid of our little $100 experiment above and start with the $100 before 1928:

The numbers get big, so you’ll need to resize the columns. You can double click on the divider between columns one at a time, or highlight multiple columns and do them all at once. I do both here, so the second one doesn’t do anything for me:

Take a guess as to how much our $100 would be worth at the end of 2019. Remember that this is a 90+ year investment! Then scroll to the bottom to see what happened to your $100.

The $100 you (well, someone else) invested in the S&P 500 at the end of 1927 is now worth over half a million dollars! That seems crazy. But, remember a couple of things:

  • Today, you can buy a fund that tracks the S&P 500 very closely. But you couldn’t in 1928. It was much more common to buy individual stocks. Some would have done much better than the index data here (Coca Cola), but some would have done much worse (Studebaker).

Still, it’s clear that you’re taking on more risk with stocks, but also getting a much better return. We’ll look more closely at stocks in the next lesson.

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Financial Literacy #10: Student Loans

We’ve looked at home mortgages. We’ve looked at credit card debt. Student Loans don’t look all that different. You borrow a large sum of money, and then you pay back the money plus a lot of interest. Student loans are just a different version of this: The payoff period is usually 10 years, and so you end up paying much less interest than with a 30-year mortgage.

One downside of student loans: They charge an origination fee, which right now is 1.059%. If you borrow $1,000 you will only get $989.41. The rest ($10.59) is a fee. Some mortgages have origination fees, but not all do.

There are lots of types of student loans. I’m far from the expert here, and so I won’t cover them all. I want to focus on one type of loan: Direct Subsidized Federal Student loans, which are awarded by the US Department of Education.

“Subsidized” is an important word here. There are also Unsubsidized student loans. With a subsidized loan, you don’t have to pay interest while you’re still in school. In effect, the interest is 0% while you’re in school.

With an unsubsidized loan, you also don’t have to make payments while you’re in school, but interest is being added to your total balance. You borrow $20,000 but by the time you start paying off the loan, the balance could be $25,000 or more. The interest-rate subsidy on a subsidized loan is a nice perk.

There are also other perks. Interest rates for the Federal loans are often lower than those you could qualify for with a loan from a private company (called a private loan). And, you may also qualify for payment forgiveness with a Federal loan, under certain circumstances. We’ll get there in a minute.

Here’s a great article in the Wall Street Journal: The Pros and Cons of Federal vs. Private Student Loans. You may not be able to read it because of the Wall Street Journal paywall. Here’s a key quote from the article: “You should never replace a federal loan with a private student loan.” The Federal Loan provides a lot of nice benefits.

Repayment Options for Federal Subsidized Student Loans

Once you are out of school and it’s time to start making payments on your loan, you have some options for the payment plans. Let’s take a look at the options, starting with the default option, called the Standard Plan.

For all of these, we’re going to use these assumptions:

You have a total balance of $20,000 in subsidized loans. You can’t borrow this much all at once with a subsidized loan; the limits are between $3,500 and $5,500 per year. After that you need to use different kinds of loans.

The interest rate on your loans is 4.53%. That was the rate for the 2019-2020 school year.

Your income after graduation is $30,000 a year, you live in Alabama, and you have no spouse or children. Okay, I know this applies to none of you. But the income-based repayment plans use your income and personal status to calculate payments.

The “Standard Plan” makes you pay off your loan in 10 years. This is exactly the same as taking out a 10-year mortgage for $20,000 with an interest rate of 4.53%. Well, except you don’t have to start paying back until after you graduate.

Try to make a spreadsheet yourself before watching me do it below. You’ll want 120 months (10 years) of payments. Monthly interest will be 4.53% divided by 12. And then change your fixed payment amount until the balance goes from $20,000 to $0 after 120 months.

Ready? Here’s how I did it:

I started my month numbers in row 3 instead of row 2; this let me start with my $20,000 loan balance in month 0, and then not make a payment until month 1. It doesn’t matter that much; I could have put the $20,000 in month 1 and gotten almost the exact same answer. I’d have to think about which one is more accurate.

Now just add the interest each month and subtract your payment. I started with a total guess of a $500 monthly payment, which it turns out is way too high:

I’m going to copy the final balance up to a cell near the top, so I can quickly see how that value changes as I change the monthly payment:

So $208 a month, or maybe a touch less. $207.57 is the closest I could get, but our math isn’t that precise. That’s not too bad; multiply that by 120 and you’ve paid a total of $24,908.40 on your $20,000 balance. Less than $5,000 in interest! And notice that even in the first month, something like 64% of your payment goes toward the principal (Our payment is $207.57, and $75.50 of that goes toward interest.) That’s the benefit of a short 10-year payoff plan and a pretty low interest rate.

Well, 10 years may not seem short when you’re the one making 120 payments, but it is short compared to a 30-year mortgage, at least!

Happily, our calculation matches the government’s figures exactly:

That’s from the nice (but a little complicated) loan simulator provided by the Federal Government.

We used the default option (The Standard Plan), which may not be the best option for you. Let’s look at a few more:

Graduated Repayment Option for Student Loan Debt

I don’t love this one. All it does is lower your payments early in the loan, and increase them later in the loan. Lower payments at first means more interest accruing, and a higher total amount you have to pay:

I’m not going to do the spreadsheet for this one, but you could try to estimate. I don’t know the formula for how much your payments increase; I just have the graph:

The payments increase every 2 years, and it looks like the increases are smaller at the beginning and larger at the end. I was able to get really close by having the payment increase by 31.5% every 2 years. So the payment goes from $117 in years 1 and 2 to $153.86 in years 3 and 4. And then to $202.32 for years 5 and 6. And so on.

If you need to lower your payments early on, then this is one option. But I think there is a much much much much better option to consider.

Income-Based Repayment of student loans: IBR

Let me start with the punchline here. Remember that you’re a single person in Alabama making $30,000 a year. Look at your payoff numbers:

What’s going on here? Our total payments under the Standard Plan were $24,908. How are you paying a bit less on your loan here but taking 20 years to do it instead of 10? The answer starts with the fact that the amount you pay is now based on your income. And that amount the government thinks you can pay is often less than the $208 dollars a month you need to pay in order to pay off the loan after 10 years.

Here, you’re paying between $91 and $113 a month. That’s about half of what you’d need to pay to get that loan down to 0 after 10 years. Here’s the key sentence: Any balance left after 20 years is waived. Gone. Here, $10,593 is forgiven.

Sadly, you will have to pay taxes on the forgiven amount. Still, you’re saving real money. Let’s lower your income to $20,000 a year:

You would pay $10 a month for the first 3 years and then … nothing else. Zero. The loan would continue accruing interest, and so your loan balance goes up and up. It gets to $37,760 and then … it disappears.

Now, you have to be very very careful here. If you suddenly get a good paying job in the year 2036, you’d need to start paying off your now large student loan balance. Even if your income slowly rises over time, you could have to pay more and more each year.

On the other hand, if you have children, the amount you would be expected to repay each year goes down.

You have to re-file each year with your income and family situation. So you’re filing 20 times with your status. That’s a hassle. Still, according to debt.org, “The Income-Based Repayment Plan, one of four debt-relief programs instituted by the federal government, might be the most attractive choice for the 73% of graduates in the Class of 2017 who left school with student loan debt.”

PAYE? REPAYE? IBR?

PAYE stands for Pay As you Earn. REPAYE is a new version of PAYE. These are also income-based payment plans that can look almost identical to the income-based option we looked at above. In fact, they are exactly identical for our sample Alabama person:

There are slight differences in the calculation, as you can see from this table:

Note that the first three all say “Generally 10 percent of your discretionary income.” You’ll have to play around with the loan simulator to see if there are any differences for your scenario. Or any future scenarios you can imagine.

PSLF: Forget about Forgiveness

Let’s complicate things one last time. If you’re in one of the income based repayment plans above, you could also qualify for PSLF, which stands for Public Service Loan Forgiveness. The idea here is that if you work in a public service field like government or education, you could get your loan wiped out in 10 years instead of 20.

You have to apply for PSLF after making payments for 10 years. The program started in 2007, and so the first people became eligible at the end of 2017.

Sadly, almost no one is getting approved:

Out of 174,495 PSLF applications submitted and processed to date, the Department of Education approved 3,174. This represents a 1.8% approval rate — slightly better than the initial statistics, but still astonishingly low.

Some of those people probably didn’t follow all of the rules, like being in an income-based repayment plan. But someone people look like they are being rejected for no good reason. Until something changes, I wouldn’t count on this working for you.

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Financial Literacy #9: Credit Cards vs. Debit Cards

In the last lesson, we looked at credit card debt and how much interest you can end up paying. Credit cards are one of the best financial tools out there if you pay your balance in full every month, and one of the worst if you don’t.

Debit cards are somewhat similar to credit cards. But there’s a big difference in how you pay for purchases. With a debit card, the bank isn’t fronting the money to the store where you make a purchase. The money comes right out of your checking account. There are no grace periods; usually the money is taken out of your account within 24 hours.

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Financial Literacy #8: A Credit Card Example

When we looked at mortgages, the payment amount was set so that the balance was paid off in 30 years. When you carry a balance on a credit card, the credit card company isn’t going to promise a payoff date. The time needed to pay off a $1,000 balance is going to vary based on the interest rate and the policies of the credit card company. Each credit card company sets your minimum payment slightly differently.

About 15 years ago, some credit cards actually had a minimum payment so low that you would never pay off your balance! If you pay less than the interest amount each month, your balance increases. This is not good.

I’m not sure whether this is still legal or not. But it almost never happens anymore, because of a clever change in the law. In 2010, the Federal Reserve started making credit card companies tell you how long it will take to pay off your balance:

Your monthly credit card bill will include information on how long it will take you to pay off your balance if you only make minimum payments. It will also tell you how much you would need to pay each month in order to pay off your balance in three years

If you would never pay off your balance, your credit card statement would need to say that, and I don’t think many companies want to say that outright! Let me know if you ever see an example of this, though.

Here’s what the new information section can look like:

Here’s the question: If you make no additional charges and pay the minimum amount each month, how long will it take you to pay off the balance? The Federal Reserve already forced your credit card company to tell you the answer: At the minimum payment level, it will take you 20 years to pay off this balance. We’re going to confirm this now.

You need some additional information before you can start working. First, the interest rate is a whopping 17.99%! That information is buried at the very end of the statement:

In this example, the account holder is paying their balance off every month, so there’s no interest being charged. Good thing, because 18% is just a silly interest rate to pay. Let’s assume from here on out you only make the minimum payment, and don’t make any additional purchases on the card.

This credit card company’s policy is that the person must pay 1% of the principal balance each month, plus whatever interest is charged. The sum of these is of course greater than just the interest payment, so the balance will go down.

But, if you keep paying 1% of the balance off each month, you never actually finish paying it off! As the balance gets smaller, your payments also get smaller. At a $100 balance, you’d pay $1 (1% of the principal) plus $1.50 in interest (18% a year is 1.5% a month, ignoring compounding.) That’s just $2.50 total. At $1 you’d pay 2.5 cents. You’d never get to $0!

To fix this problem, the credit card company set a minimum payment amount of $25. As soon as you get below a $25 payment, the percentage of the principal that you pay off each month increases. And at a balance of $24.63 or so, you’d still pay that minimum of $25, which would bring your balance to $0 ($24.63 in principal plus $0.37 in interest.)

This spreadsheet will be more complicated than the mortgage spreadsheet, since we need to determine whether or not that $25 minimum kicks in for any given month. And, it’s going to have a lot more rows since we’re going to look at monthly payments for the first time.

First, create a month column, and make sure you have 240(!) numbers there. Add in the starting principal, and the payment (before interest) of 1%.

I probably should have labeled column C something besides Payment, since this isn’t your total payment. It’s really just a working column … maybe “Working Principal Payment”?

Next, let’s add in our constant for the interest rate, and then the interest. The sum of the Payment plus Interest is the actual payment, unless that’s less than $25. We’re going to use the Max function, which returns the larger of a set of values.

Here are a couple of examples of how the Max function works:

=Max(1, 3) returns 3.

=Max(3, 1) also returns 3.

=Max(3,1,3,4,3,1,2,3,4,1) returns 4. Max doesn’t care about the number of numbers in there, or their order, or if there are duplicates.

In the first row above, the formula in E2 for the actual payment simplifies like this:

=MAX(25,C2+D2)
=MAX(25, 56+85.15)
=MAX(25, 141.15)
=141.15

Next month, the comparison will be:
=MAX(25, 140.31)

The second number keeps getting smaller until eventually 25 is larger. Then MAX will return 25 for the rest of the rows.

Now all we have to do is set next month’s principal lower by the amount of principal we paid off. Note that we don’t apply the total payment as a reduction in the principal– the interest payment just goes to the bank!

Here’s where that $25 minimum gets confusing. The amount of principal we pay down isn’t just the value in column C. It is exactly that value for the first payments. But eventually, once the $25 minimum kicks in, the principal payment is more than the small value in Column C. Scroll down and see when that $25 kicks in:


Notice I used the Freeze Panes button. My cursor was in cell A2 before I pressed Freeze Panes. This leaves row 1 frozen, so I can see my header labels as I scroll down. (If you’re using Google Sheets, click on a call in row 2 and then choose View–> Freeze–> 1 row.

Notice how once the actual payment is fixed at $25, the amount of that $25 that goes to principal increases each month. This makes sense: as the balance goes down, the interest I owe goes down. Since the payment stays fixed, more of that payment can go to principal. You can graph column F to see how this kicks in:

I forgot to answer the question. How long does it take to pay off your balance? Scroll down and see when the principal is finally paid off. I see the last positive balance at month 235. Divide 235 months by 12 and that’s 19.583 years, which rounds to 20 years. Just like the credit card company told us!

This isn’t so important, but you can try one more thing if you don’t have spreadsheet fatigue yet. Notice that the minimum payment in the first image was exactly $56:

The credit card company makes you pay 1% toward the principal, but they round down to the nearest dollar. We can use the ROUNDDOWN function to get even more accurate:

=ROUNDDOWN(B2*1%,0) says to round the value down, and leave 0 decimal places. The truncate function would also do the same thing: =TRUNC(B2*1%,0)

Now our principal payments are a little bit lower each month, or at least never higher. So it should take even longer to pay off the balance. And when I scroll down, now it takes until month 239 until the balance is paid off. 240 is exactly 20 years, so we’re right at 20 years now.

You can use the spreadsheet to see how much you paid in interest. I see about $7,686 in interest, and about $13,366 of total payments (interest plus the initial principal amount.) This is very close to the image above; it’s within $60 of the value the credit card company says.

These numbers aren’t that different from a mortgage! At 6% we paid a $117,000 in interest on a $100,000 principal. Here we paid $7,686 in interest on a $5,680 balance. The difference is the 1% principal payment each month. At the beginning of the mortgage, you’re only paying off 0.11% of the principal each month! Lower payments mostly cancel out the lower interest rate.

But there is one fundamental difference between a mortgage and credit card debt: Your mortgage is paying for an asset that usually retains or increases in value, which most credit card purchases decrease in value!

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Financial Literacy #7: Introduction to Credit Cards

So far everything has been quite clearly positive or negative to your finances. Money in the bank earning interest gis helpful. Paying off the interest on a mortgage is not helpful (though buying the house can be good over the long-term!)

Credit cards are a different story. They are either positive for your finances, or a very big negative. And the exact same card can be either, depending upon how you use it.

If you’re in High School, you may not need this information for a little while: Unless you prove you have income, you can’t get your own credit card until you turn 21.

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Financial Literacy #6: A Focus on Mortgages

Let’s look at our mortgage example some more. We already know that 83% of your payment the first year ends up just paying off the interest. The good news is that this number steadily decreases with each payment. This makes sense: You pay the same fixed amount each year, but the loan balance decreases each year. A lower balance means less interest. Less interest, same payment … so more of the money can go to paying off the mortgage balance.

Before we get started, I didn’t leave quite enough room for all of the columns I want. Let’s cut and paste our constants over 1 column:

Once you highlight the cells, cut them, move over a column, and paste. It’s easier to use keyboard shortcuts here: CTRL + X to cut, and CTRL + V to paste.

I also added a Payment column above. This is just copying the one payment constant down for each of our 30 years.

Now let’s add 2 more columns: The interest paid each year, and then the ratio between the two. The ration is the percentage of the payment that goes toward interest. We already know that the first year should be 83%.

Notice that I put a negative sign in front of D2 in the Ratio formula; it’s hard to see. If you leave it out it’s not a big deal, but a ratio of -83% might be confusing.

Notice how the ratio goes down consistently. By the end, just 5.6% of your payment is going toward interest– that’s the 0.056357 number in cell E31. We’ll change the format of this number to be a percentage in a minute. But first, let’s add up how much you paid in total over 30 years, and how much of that went to interest:

SUM is a spreadsheet function that adds any numbers it finds in a range of cells. Excel or Google Sheets will automatically add the close parenthesis for you when you hit enter after you choose the range.

Look at your sums. Over 30 years, you’ve paid $217,950 in total payments, and $117,941 in interest. The difference between those is just over $100,000– that’s the amount of the mortgage principal you paid back! (It’s not exactly $100,000 because we ended up with an over-payment of $8.61 at the end.)

You paid more in interest than the loan value itself! $117,900 in interest for your $100,000 loan. Seems crazy, doesn’t it? This is common for mortgages, where most people can’t afford to pay in cash. Where it’s less of a good idea is with a credit card payment. Whatever you buy on your credit card can easily cost you 2 or 3 times more with interest payments over time. More on this in the next lesson.

The good news is that with lower interest rates, mortgage rates aren’t 6% today. Take a look at Bank of America’s mortgage rates today. Or any bank; I chose Bank of America because they show you the rates without asking for any personal information.

Look at the APR, which builds in all the fees, such as points. We’re not going to get into points here, but basically a point costs you money up front in exchange for a lower interest rate. Pay more now to pay less later.

Here’s what I see. I asked for a $100,000 loan just to match our spreadsheet:

So 3.63%. You can use that, or 3.5% (as I do below) or whatever rate you see today. Before we enter that rate, let’s add some decimal places to our interest rate constant. Otherwise, Excel will round 3.5% to 4%.

With a lower interest rate our payments can be lower. Decrease the annual payment amount in cell G1 until you get to $0 or so after 30 years. What are your total payments now? Do you pay more or less than $100,000 in interest now?

Let’s do 2 more examples. At 6%, we paid $117,000 in interest. At 3.5% or so, we paid under $100,000 in interest. Just for fun, at what interest rate would you pay exactly $100,000 in interest?

You could try different interest rates, but for each one you would then need to change the annual payment amount. That would take a lot of time. But you know something about this case: If you’re paying $100,000 for the house, and $100,000 in interest, your total payments are $200,000.

So let’s change the payment constant so you pay a total of $200,000 over 30 years. The annual payment is simply 200,000 divided by 30:

Then increase the interest rate until you get to that $0 balance after 30 years.

One final example. Remember that in the early years, very little of your payment goes toward paying down the principal. It all goes to paying off that year’s interest. You’re allowed to make extra payments early on, which would go toward principal. (A few mortgages don’t allow for pre-payments. If you find a mortgage that charges a pre-payment penalty, don’t take it!

Let’s say you make an extra payment of $100 in the first year. Just that one payment, and then you just pay the regular amount every year after that. How much does that save you in interest?

I went back to my 6% interest example for this, but you can use any scenario you want.

That’s it– don’t double click to copy the new formula down! Well, you can, but that would be the case where you make an extra $100 payment every year.

How much has the balance at the end increased? Does that seem like a lot?

Here, compound interest is working in our favor, at least on that $100. This is the equivalent to investing $100 at a 6% interest rate. We’re back to the very first lesson! That $100 is going to compound to a much bigger value over 30 years. Those early principal payments can make a big difference.