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?
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.
