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An investment is advertised as returning 2.5% every 6 months (semiannually), compounded semiannually. If $20,000 is invested, the growth can be modeled by the equation A(t) = 20,000(1.025)^2t. What is the equivalent annual growth rate for this investment (rounded to the nearest hundredth of a percent) and what is it worth (rounded to the nearest thousand dollar) after 30 years?

Hint: Find the value of 1.025^2 on your calculator.

 

A. 5.01% and $86,000
B. 5.06% and $88,000
C. 51.30% and $30,000
D. 75.01% and $70,000

 Feb 24, 2016
 #1
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We can find the annual growth rate as follows :

 

(1.025)^60  = ( 1+r)^30     taking logs and simplifying, we hace

 

60 log 1.025  = 30 log (1 + r)

 

2log (1.025)  = log ( 1 + r)

 

This says  that

 

10^[2log(1.025)] = r + 1

 

10^[2log (1.025) ] - 1  = r   = about   .0506  = about 5.06%

 

Thus, B must be the correct answer

 

 

cool cool cool

 Feb 24, 2016

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