Math Problem Statement

(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

Solution

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

12×t=12t12 \times t = 12t

So, the growth factor will need to be applied 12t12t times in tt 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 tt for time in years?
  2. What happens to the total interest earned if tt is doubled?
  3. How does the growth factor change with different values of tt?
  4. How would the number of compounding periods change if the interest were compounded quarterly instead of monthly?
  5. What impact does increasing tt 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.

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth

Formulas

Compound Interest Formula

Theorems

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Suitable Grade Level

High School