Math Problem Statement

If an initial investment of $2,800 grows to $35,000 in 18 years, what annual interest rate (as a %) compounded annually did this investment earn? (Round your answer to two decimal places.) %

Solution

To determine the annual interest rate for this investment compounded annually, we can use the formula for compound interest:

A=P(1+r)tA = P(1 + r)^t

Where:

  • AA is the final amount ($35,000),
  • PP is the initial principal ($2,800),
  • rr is the annual interest rate (which we need to find),
  • tt is the time in years (18 years).

Rearranging the formula to solve for rr:

r=(AP)1t1r = \left( \frac{A}{P} \right)^{\frac{1}{t}} - 1

Now, let's plug in the values:

r=(35,0002,800)1181r = \left( \frac{35,000}{2,800} \right)^{\frac{1}{18}} - 1

I'll calculate this now.The annual interest rate, compounded annually, is approximately 15.06%.

Would you like further details on this calculation or have any other questions?

Here are 5 related questions to deepen your understanding:

  1. How does the time period affect the growth of an investment with compound interest?
  2. What is the difference between simple and compound interest?
  3. How would the annual interest rate change if the investment period were shorter, say 10 years?
  4. What is continuous compounding, and how does it differ from annual compounding?
  5. How can you calculate the future value of an investment with monthly compounding?

Tip: Always remember, the frequency of compounding can significantly impact the growth of an investment over time!

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth

Formulas

Compound Interest Formula: A = P(1 + r)^t
Rearranged Formula: r = (A/P)^(1/t) - 1

Theorems

Compound Interest Theorem

Suitable Grade Level

Grades 11-12 (Advanced Algebra or Pre-Calculus)