Math Problem Statement
Use the compound interest formula AequalsP(1plusr)Superscript t and the given information to solve for r. Aequals$2200, Pequals$1700, tequals4 Question content area bottom Part 1 requals enter your response here% (Round to the nearest hundredth.)
Solution
The compound interest formula is:
Where:
- is the final amount (2200 in this case),
- is the principal amount (1700 in this case),
- is the annual interest rate (which we are solving for),
- is the time the money is invested or borrowed for (4 years here).
We are given:
Now, plug the values into the formula:
Step 1: Divide both sides of the equation by 1700 to isolate :
Step 2: Take the fourth root of both sides to eliminate the exponent:
Step 3: Subtract 1 from both sides to solve for :
Step 4: Convert this decimal to a percentage by multiplying by 100:
So, the annual interest rate is approximately 6.52%.
Let me know if you'd like further details or have any questions!
Here are some related questions to explore further:
- How would the interest rate change if the time were different, say 5 years?
- How do you calculate compound interest if interest is compounded more frequently than annually?
- What would the final amount be if the principal was $2000 with the same rate and time?
- How do you derive the compound interest formula from the simple interest formula?
- How does compound interest differ from simple interest in terms of growth over time?
Tip: When solving for an unknown in an exponentiation equation like this, remember to isolate the base first and then apply the appropriate root or logarithmic function to solve.
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Math Problem Analysis
Mathematical Concepts
Compound Interest
Algebra
Exponents
Formulas
A = P(1 + r)^t
Theorems
Compound Interest Theorem
Suitable Grade Level
Grades 9-12
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