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?
:
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*(1+(i/2))^2}}} = resulting amt compounded semi-annually
;
{{{a*(1+(i/2))^2}}} = 1.09a
simplify, divide both sides by a
{{{(1+(i/2))^2}}} = 1.09
find the square root of both sides
1 + {{{i/2}}} = {{{sqrt(1.09)}}}
{{{i/2}}} = {{{sqrt(1.09)}}} - 1
multiply both sides by 2
i = {{{2(sqrt(1.09)-1)}}}
using your calc
i = .08806 or 8.8% equiv compound interest