请问为什么不能用选项B的算法？

问题如下：

Question A bank offers an effective annual rate (EAR) of 12%. Assuming quarterly compounding, the stated annual interest rate is closest to:

选项：

A.11.66%. B.12.55%. C.11.49%.

解释：

Solution

C is correct. First, find the periodic interest rate by rearranging the following formula:

EAR = (1 + Periodic interest rate)^m -1

12.00% = (1 + Periodic interest rate)⁴ -1

By solving for the periodic interest rate we obtain:

Periodic interest rate = $\sqrt[4]{\left(12.00\%+1\right)}?1$ = 2.873734%

Then, find the stated annual interest rate as follows:

Stated annual interest rate = Periodic interest rate × m

= 2.873734% × 4

= 11.49%

A is incorrect. It uses semiannual rather than quarterly compounding:

12.00% = (1 + Periodic interest rate)² -1

By solving for the periodic interest rate we obtain:

Periodic interest rate = $\sqrt[2]{\left(12.00\%+1\right)}?1$ = 5.83%

Then, find the stated annual interest rate as follows:

Stated annual interest rate = 5.83% × 2 = 11.66%

B is incorrect. It uses the following formula:

${\left(1+\frac{12.00\%}{4}\right)}^4?1$ = 12.55%