SOLUTION: Suppose that a savings account pays an effective rate of interest of 9 percent. What is the equivalent annual compound interest rate if interest is compounded semi-annually? Tha

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Question 1160384: Suppose that a savings account pays an effective rate of interest of 9 percent. What is the equivalent annual compound interest rate if interest is compounded semi-annually?
Thank you for any help in advance!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that a savings account pays an effective rate of interest of 9 percent.
What is the equivalent annual compound interest rate if interest is compounded semi-annually?
:
Let a = the initial amt of the account
let i = the equiv interest rate
then the resulting annual amt = 1.09a
Compounded semi-annually
a%2A%281%2B%28i%2F2%29%29%5E2 = resulting amt compounded semi-annually
;
a%2A%281%2B%28i%2F2%29%29%5E2 = 1.09a
simplify, divide both sides by a
%281%2B%28i%2F2%29%29%5E2 = 1.09
find the square root of both sides
1 + i%2F2 = sqrt%281.09%29
i%2F2 = sqrt%281.09%29 - 1
multiply both sides by 2
i = 2%28sqrt%281.09%29-1%29
using your calc
i = .08806 or 8.8% equiv compound interest