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Explain the difference between an investment that increases at 5% monthly versus one that increases at 5% annual rate compounded monthly. Which annual growth rate would be larger? What are the annual growth rates in each case?

 Sep 30, 2020
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1 - 5% compounded monthly is the same as: 5 x 12 months =60% annual rate compounded monthly. So, if you started the year with 1,000 dollars and got 60% annual rate compounded monthly, this is how much you would have at the end of the year: FV = 1,000 x (1 + 60/1200)^12 =1,795.86. [I'm assuming the end of each month].

 

2 - 5% annual rate compounded monthly is 0.05 / 12 =0.41667% - this is the monthly compound rate. So again, if you started the year with 1,000 dollars, this is how much you would have at the end of the year:

FV =1,000 x (1 + 0.41667/100) =1,051.16.

 

3 - The difference of 1795.86 - 1,051.16 =744.70 - this is very, very large difference for 1 year investment on 1,000 dollars.

 Sep 30, 2020

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