Growth Rate Applications



True or False?
Know equations on page 45 & 49 (of Jones Macro Econ Crisis Update Ed).
You’ll almost certainly get a problem like this on your exam, just different numbers.

            



You have two options, which do you prefer?


With a calculator:
Option 1:
--OR-- Option 2:

Calculator Method 1)
Assume you want the more valuable option and assume that you've memorized (for life) the equation on page 45,

Now, which option is bigger?

Option 1:



Option 2: $110 

Option 1 is bigger. You’d prefer option 1 is preferred. True.



Calculator Method 2)
Alternatively, you can use the equation you know and love on page 49, calculate the ‘net-present value’ of option two.


Option 1
:


Option 2: Worth $110 in five years
     
    
     



Clearly the $100 today is better than the equivalent of $86 today. You prefer option 1. True.



Now – Without A Calculator
You should be able to look at the options and know the first option is better.
Say you get option 1, you get $100 today, at 5% interest.
  • Year 1) If you wanted to, you could put that cash in the bank, this year you’d earn 5%, or an extra $5 for a total of $105.
  • Year 2) Next year, you’d earn 5% on your $105. So you’d earn over $5. You’re balance now more than $110.
  • Year 3) The following year (year 3), you’d earn another 5% on that +$110. So, with compound interest you’d have Over $115 in the bank.
  • Year 4) ...and so on...
  • Year 5) After 5 years you can assume you’d have over $125.
~In fact! If your options where Option 1: Today: $100 at 5% or Option 2: In Five Years $125 – You should know that option 1 gives you compound interest; delivering in five years over $125.  

Making it clear Option 1 is the better of the two options.   -----TRUE!



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