Math Problem Statement

​(B) If it is compounded​ quarterly, what is the​ amount? ​$    enter your response here ​(Round to the nearest​ cent.)

Solution

To calculate the amount of money after interest is compounded quarterly, we use the compound interest formula:

A=P(1+rn)ntA = P \left(1 + \frac{r}{n}\right)^{nt}

Where:

  • AA is the amount of money accumulated after interest (including principal),
  • PP is the principal amount (initial investment),
  • rr is the annual interest rate (in decimal form),
  • nn is the number of times the interest is compounded per year,
  • tt is the number of years the money is invested or borrowed for.

To help you with the calculation, I need the following information:

  • Principal amount (PP),
  • Annual interest rate (rr),
  • Number of years (tt).

Once you provide that, I can calculate the final amount for you.

Let me know if you want further explanation or clarification!

Here are some related questions for you to consider:

  1. What is the difference between simple interest and compound interest?
  2. How does the frequency of compounding (quarterly, monthly, annually) affect the final amount?
  3. How can you calculate compound interest if it is compounded continuously?
  4. What happens if the interest rate is changed during the investment period?
  5. How would you use this formula for loan calculations?

Tip: Always check that the interest rate is in decimal form when plugging it into the formula! For example, 5% should be written as 0.05.

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth

Formulas

A = P(1 + r/n)^(nt)

Theorems

Compound Interest Theorem

Suitable Grade Level

Grades 9-12