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Select the value in the expression that represents the number of times per year that interest is compounded on the account.

Rick uses this exponential expression to determine what the value of his bank account will be in three years:

[tex]\[5,000\left(1+\frac{0.04}{12}\right)^{12t}\][/tex]

Sagot :

GinnyAnsweridn
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.
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