(c) If interest is compounded monthly, how many times would the growth factor be applied in *t* years?

The growth factor will need to be applied  times in *t* years

If interest is compounded monthly, the growth factor is applied once per month. Therefore, in \( t \) years, the growth factor will be applied:

\[
12 \times t = 12t
\]

So, the growth factor will need to be applied **\( 12t \)** times in \( t \) years.

Would you like further explanation or have any other questions? Here are some related questions:

1. How would you express the compound interest formula with a variable \( t \) for time in years?
2. What happens to the total interest earned if \( t \) is doubled?
3. How does the growth factor change with different values of \( t \)?
4. How would the number of compounding periods change if the interest were compounded quarterly instead of monthly?
5. What impact does increasing \( t \) have on the overall growth of an investment?

**Tip:** Always express the number of compounding periods as a product of the frequency (e.g., monthly, quarterly) and the time period in years. This helps in accurately calculating interest.

Explore how compound interest works with monthly compounding. Learn how many times the growth factor is applied in 't' years using the compound interest formula. Suitable for high school students studying financial mathematics.

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