In order to compare investments, analysts will convert monthly, quarterly, semi-annual rates to annual rates. If an investment of $100,000 is invested at 4.5% twice a year compounded semi-annually, the growth can be modeled by the equation A(t)=100,000(1.045)2t. What is the equivalent annual growth rate for this investment (rounded to the nearest tenth of a percent) and what is it worth (rounded to the nearest whole dollar) after 15 years?
a. 2.2%, and $139,114
c. 9.2% and $374,532

 Jan 16, 2019

The equivalent annual growth rate would be  

   wait a minute....this makes me a bit confused:     $100,000 is invested at 4.5% twice a year compounded semi-annually(

 (I think this means you get 4.5% added to your investment  each 6 months....yah? I think this would be the same as 9% compounded semi)

Assuming you have the correct equation, at the end of ONE year

A = 100000(1.045)^2 = 109202.5        which is 9.2% growth  per year


At 15 years      A = 100000(1.045)^2(15)    = $374531.81 ~$ 374,532

 Jan 16, 2019
edited by ElectricPavlov  Jan 16, 2019
edited by ElectricPavlov  Jan 16, 2019

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