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?

Answer 1

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 used in the calculation of compound interest.

Here's the breakdown:

- The \( 0.03 \) represents the annual interest rate, which is 3%.
- The division by \( 12 \) indicates that this annual interest is being converted to a monthly rate since there are 12 months in a year.

Therefore, \( \frac{0.03}{12} \) calculates the interest rate per month. Specifically, it means that for every month, the amount in the savings account earns interest at a rate of \( 0.03/12 \) or \( 0.0025 \) (which is 0.25%). This rate is compounded monthly, which is important for determining the total amount \( A \) in the account after \( t \) years.