To determine the value in the expression [tex]\(5,000\left(1+\frac{0.04}{12}\right)^{12 t}\)[/tex] that represents the number of times per year that interest is compounded, let's analyze each component of the expression step-by-step:
1. Principal Amount: The term [tex]\(5,000\)[/tex] represents the initial amount of money deposited in the bank account.
2. Interest Rate: The [tex]\(0.04\)[/tex] in the fraction represents an annual interest rate of 4%.
3. Compounding Frequency: In the fraction [tex]\(\frac{0.04}{12}\)[/tex], the denominator 12 signifies the number of times interest is compounded per year.
4. Exponential Term: The exponent [tex]\(12t\)[/tex] combines the number of times interest is compounded per year (12) and the number of years [tex]\(t\)[/tex] that the money is invested.
To summarize, the value in the expression that represents the number of times per year that interest is compounded is 12.
