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:
Where:
- is the final amount ($35,000),
- is the initial principal ($2,800),
- is the annual interest rate (which we need to find),
- is the time in years (18 years).
Rearranging the formula to solve for :
Now, let's plug in the values:
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:
- How does the time period affect the growth of an investment with compound interest?
- What is the difference between simple and compound interest?
- How would the annual interest rate change if the investment period were shorter, say 10 years?
- What is continuous compounding, and how does it differ from annual compounding?
- 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)
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