+157 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
+128732 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
