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Suppose that a savings account pays an effective rate of interest of 9.3 percent.
What is the equivalent semiannual compound interest rate ?
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It is reduced to solving this quadratic equation
1.093 = (1 + r/2)^2.
In other words, they want you find the solution r to this quadratic equation.
Simplify it
1.093 = 1 + r +
0.093 = r +
4*0.093 = 4r + r^2
r^2 + 4r - 0.372 = 0
Use the quadratic formula and get the solution.
Of the two possivle roots, one is positive, the other is negative.
Choose the positive root r = 0.09093..., or r = 0.09 (rounded).
ANSWER. The rounded equivalent semiannual compound interest rate is 0.09, or 9%.
CHECK. = 1.0920, which is close enough.
Solved.