a customer deposited an amount of money, $a$, in a bank that pays 4% annual interest, compounded…

a customer deposited an amount of money, $a$, in a bank that pays 4% annual interest, compounded semiannually, as shown in the expression. in the expression, $t$ represents the number of years the money is in the account. enter the number that completes the expression. enter your answer in the box. $a(1 + \frac{0.04}{2})^{2t}=a(square)^{t}$

a customer deposited an amount of money, $a$, in a bank that pays 4% annual interest, compounded semiannually, as shown in the expression. in the expression, $t$ represents the number of years the money is in the account. enter the number that completes the expression. enter your answer in the box. $a(1 + \frac{0.04}{2})^{2t}=a(square)^{t}$

Answer

Explanation:

Step1: Simplify the left - hand side exponent

First, simplify the expression inside the parentheses of $A\left(1+\frac{0.04}{2}\right)^{2t}$. Calculate $1+\frac{0.04}{2}=1 + 0.02=1.02$. So the left - hand side is $A(1.02)^{2t}$.

Step2: Use exponent rule

According to the exponent rule $(a^{m})^{n}=a^{mn}$, we can rewrite $A(1.02)^{2t}$ as $A((1.02)^{2})^{t}$.

Step3: Calculate $(1.02)^{2}$

Calculate $(1.02)^{2}=1.02\times1.02 = 1.0404$.

Answer:

$1.0404$