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Who can focus on math when there's all that candy waiting to be collected? Today we spent all day on the in class problems. I'm continuing to try to new class formats to make sure that everyone is challenged but nobody is left behind. I let the kids work on 8 problems for 15 minutes. I expected some to finish one or two and some to finish 6. Then we started with number 1. If you got it right, keep working on your own. If you got it wrong, we worked it out together. Then we got to number 2 and did the same thing. If you hear any complaints about pacing (either this class or prior classes), please let me know!
Class Materials - In class problems
here
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(solutions at the back).
Extra MO Problems -
Here
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. Problems, problems with hints, and then solutions.
Mailing List - Math loving friends can sign up
here
⁠
or email me at rbarrows@alum.mit.edu
Math In The Real World (
pdf
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)

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Retire Early
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Why work a job you don’t like when you’re 50, when you can just retire and surf all day instead? We’ll discover the miracle of compound interest.
Who has a bank account?
Who has a college savings account?
Who knows what interest means?
If you have $100 in your account, how much interest will you get each year? It depends what the interest rate is. If it's regular savings account, that's about 2%, so you'd get $2 every year in interest. When interest rates are high, this can be more like $10. When they are low it can be $0.
If you put your $100 in the stock market, how much do you think you'll get in a year?
What about in a really good year? What about in a really bad year?
You guys are all about 10. Let's say you put your $100 in the stock market now and it returns 10% per year. How much will you have next year? How much will you have in 7 years when you're a senior? $201.38
Let's take a quick break here and notice something cool. Your money basically doubled in seven years. There is this neat trick called the Rule of 72.
The Rule of 72
You can use it to find out how long it will take for you to double your money at a certain interest rate. The formula is:
For your money to double: Interest Rate * Time = 72
So in this case, we said the interest rate was 10%, so the Time must be 7.2 years (approximately).
What if your interest rate was only 8% instead of 10%. How long would you need to wait for your money to double?
Yes, about 9 years.
What if your Interest rate was only 3.6%? Yikes, about 20 years! Now you know why everyone is complaining that interest rates are too low. They are about 2% right now, so we'll need 36 years to double our money.
Your money doubled and you didn't even do anything. That's great. But that's not the point of the lecture. We're trying to get you retired. Nobody is going to retire on $200. How much would your $100 be worth when you turn 50? Any guesses? Almost $5,500! 5459.82
Now we're getting somewhere. $5,500 is a lot better than $100, but again, nobody is going to retire on $5,500. But all you did was put $100 in your account now and then did nothing ever again. What if you weren't so lazy? Do you think you could increase your contributions by 10% next year? So you'd have to save $110 and add that to your account. And you could probably increase that by 10% every year as you got older too, right? Who has a guess for how much money they'd have when they turned 18 if they did this? $2,400.

How about when you turn 50? $204,000!
The Miracle Of Compound Interest
This is a miracle right? But this isn't nearly as good as it can be. Each one of you should be able to retire when you're 40, if that's something you want to do. Not everybody makes this a priority, but you could. Some people would rather have nice cars, a beach house, luxury vacations, etc. That's fine, but you could also choose to save that money and retire instead. Most of you will be able to save $600 when you're 18, $4,000 when you get your first job out of college at 22, $18,000 when you turn 30, etc. If you follow this table, you'll be at a cool 1 million dollars when you turn 40. Now you're ready to retire and play Fortnite all day, or surf, or start a band, or whatever it is you want to do. This is called the Miracle of Compound Interest. There are quotes of Albert Einstein saying Compound Interest is the most powerful force in the universe (he didn't actually say it though). This rich old guy named Warren Buffett praises compound interest all the time. He's the 4th richest person in America with over $80 billion compounding right now for him.

Money Grows All By Itself

1
10
$100.00
$11.00
$111.00
2
11
$111.00
$12.00
$122.00
3
12
$122.00
$13.00
$135.00
4
18
$223.00
$23.00
$246.00
5
22
$332.00
$35.00
$367.00
6
30
$739.00
$78.00
$817.00
7
40
$2,009.00
$211.00
$2,220.00
8
50
$5,460.00
$574.00
$6,034.00
9
70
$40,343.00
$4,243.00
$44,586.00
10
100
$810,308.00
$85,221.00
$895,529.00
There are no rows in this table
⁠

Money Skyrockets With Contributions

1
10
$100.00
$110.00
$11.00
$221.00
2
11
$221.00
$121.00
$23.00
$365.00
3
12
$365.00
$133.00
$38.00
$536.00
4
18
$1,966.00
$236.00
$207.00
$2,408.00
5
22
$4,197.00
$345.00
$441.00
$4,984.00
6
30
$14,812.00
$740.00
$1,558.00
$17,110.00
7
40
$58,087.00
$1,919.00
$6,109.00
$66,115.00
8
50
$204,124.00
$4,979.00
$21,468.00
$230,571.00
9
70
$2,145,228.00
$33,493.00
$225,616.00
$2,404,336.00
10
100
$60,162,775.00
$584,432.00
$6,327,374.00
$67,074,582.00
There are no rows in this table
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Most Of You Can Retire At 40

1
10
$100.00
$110.00
$11.00
$221.00
2
11
$221.00
$121.00
$23.00
$365.00
3
18
$2,368.00
$600.00
$249.00
$3,217.00
4
22
$9,774.00
$4,000.00
$1,028.00
$14,802.00
5
25
$29,105.00
$6,000.00
$3,061.00
$38,166.00
6
30
$105,640.00
$18,000.00
$11,110.00
$134,751.00
7
35
$330,633.00
$40,000.00
$34,773.00
$405,406.00
8
40
$847,893.00
$66,550.00
$89,174.00
$1,003,616.00
There are no rows in this table
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