Hello,

Here's an easy way to look at this:

Assuming simple interest: Assuming simple interest of 20% for 5 years, that's $100 * 20% = $20 per year => $100 for 5 years

This will be $100+$100 = $200.

Adding the extra bit for compounding: 

20% of 20 is 4. Doing that for 4 years is $16 - lets call this A

Doing that for 3 years is $12 - B

Doing that for 2 years is $8 - C

Doing that for 1 year is $4 - D

Now, A + B + C + D = $40

This gives you a ‘simple interest estimate for compounding’ at $40. Thus with true compounding, the answer would be a little over $240.

Adding some thoughts..

1. Try using Rule of 72 as a proxy for CAGR numbers - see how long it takes to double a number and then add / subtract 1-2 years from there.

2. You can just take linear growth and then adjust from there. You know it must be higher, if linear growth already gets you to 200. Compounding effect is stronger, so it can't be less than the 200.

3. For simple examples with “pleasant” growth rates like 10%, 20% or 50% and a relatively short timeframe, can just quickly do it manually. Here what it would look like is: 1) 100 x 1.2 = 120 x 1.2 = 144 x 1.20 = 173 x 1.2 = 207 x 1.2 = 248 → adding 20% increments should be fairly quick 

what I don't get is the consumption. why is he drinking just 72 bottles a year after year 5? initially he said 8 bottles to drink and 2 as a gift = 10 bottles a month = 120 bottles consumption a year. but if he buys only 72 a year and consumes 120 the graph should fall….. where do I have a thinking gap?

(edited)