Question

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

Answer 1

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

`1500\lbrack(1+(0.05)/(12))^(12)\rbrack^4`

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

`(a^x)^y=a^(x\cdot y)`

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

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

Therefore, the equivalent expression is

`1500(1+(0.05)/(12))^(48)`

Option D is the correct answer.