Question
The expression A = 10,000 (1+ 0,03/12)^12t
represents the amount, A, in a saving account after t years.
What is the meaning of 0.03/12 in the expression?
represents the amount, A, in a saving account after t years.
What is the meaning of 0.03/12 in the expression?
Answers
GPT-4o mini
In the expression \( A = 10,000 \left(1 + \frac{0.03}{12}\right)^{12t} \), the term \( \frac{0.03}{12} \) represents the monthly interest rate when the annual interest rate is 3% (0.03).
Here's the breakdown:
- The annual interest rate is given as 3%, which can be expressed as a decimal: \( 0.03 \).
- Since interest is compounded monthly, the annual rate needs to be divided by the number of months in a year (12). Thus, \( \frac{0.03}{12} \) calculates the interest rate applied each month.
Therefore, \( \frac{0.03}{12} \) determines how much interest is added to the account balance each month, which contributes to the compounding effect on the total amount \( A \) over time.
Here's the breakdown:
- The annual interest rate is given as 3%, which can be expressed as a decimal: \( 0.03 \).
- Since interest is compounded monthly, the annual rate needs to be divided by the number of months in a year (12). Thus, \( \frac{0.03}{12} \) calculates the interest rate applied each month.
Therefore, \( \frac{0.03}{12} \) determines how much interest is added to the account balance each month, which contributes to the compounding effect on the total amount \( A \) over time.