Question bank / Equivalent expressions

Math · Advanced MathHard

Which of the following expressions is equivalent to 1,200(1.06)t1{,}200(1.06)^t?

A

1,200(1.005)12t1{,}200(1.005)^{12t}

B

1,200(1.06)12t1{,}200(1.06)^{12t}

C

1,200(1.0612)12t1{,}200\left(\frac{1.06}{12}\right)^{12t}

D

1,200(1.06112)12t1{,}200\left(1.06^{\frac{1}{12}}\right)^{12t}

Show answer and explanation

Answer: D

By the power of a power rule, (1.06112)12t=1.0612t12=1.06t\left(1.06^{\frac{1}{12}}\right)^{12t} = 1.06^{\frac{12t}{12}} = 1.06^t. So choice D is equivalent. Choice A is not equivalent because (1.005)12≈1.0617(1.005)^{12} \approx 1.0617, not exactly 1.061.06.

Choice A divides the 6% rate by 12, which is a common estimate, but compounding makes (1.005)12(1.005)^{12} slightly larger than 1.061.06.

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