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This expression represents the amount of money, in dollars, that will be in a savings account after 4 years.1500 [1 + 0.05/12)^12]^4Which of these is equivalent to the expression?A). 1500 (1.05/12)^48B). 1500 (1.05/12)^16C). 1500 (1 +0.05/12)^16D). 1500 (1 + 0.05/12)^48

Respuesta :

The expression below represents the amount of money, in dollars, that will be in a savings account after 4 years.

[tex]1500\lbrack(1+\frac{0.05}{12})^{12}\rbrack^4[/tex]

Recall from the laws of exponents, the power of a power rule is given by

[tex](a^x)^y=a^{x\cdot y}[/tex]

So applying the above rule on the given expression, we get

[tex]\begin{gathered} 1500\lbrack(1+\frac{0.05}{12})^{12}\rbrack^4 \\ 1500(1+\frac{0.05}{12})^{12\cdot4} \\ 1500(1+\frac{0.05}{12})^{48} \end{gathered}[/tex]

Therefore, the equivalent expression is

[tex]1500(1+\frac{0.05}{12})^{48}[/tex]

Option D is the correct answer.

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