Math Problem Statement
Solution
This problem involves calculating the total balance in two accounts:
- An investment account that compounds monthly with a 6% annual interest rate.
- A savings account with a constant balance of $800.
Breaking Down the Problem:
- The formula for compound interest is:
where:
= principal amount ($200),
= annual interest rate (6% = 0.06),
= number of compounding periods per year (12 for monthly),
= number of years.
Thus, the balance of the investment account after years is:
- Adding the savings account balance of $800, the total balance becomes:
Correct Answer:
The correct choice is:
Let me know if you want further clarification!
Here are 5 related questions to expand your understanding:
- What happens to the total balance if the savings account increases by $100 annually?
- How does the compounding frequency affect the total balance in the investment account?
- If the interest rate is increased to 8%, how would that change the formula?
- How can you graph to visualize the growth over time?
- What is the balance after 5 years?
Tip: Always confirm the compounding frequency when working with compound interest problems—it directly impacts the formula and the results.
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Math Problem Analysis
Mathematical Concepts
Compound Interest
Exponential Growth
Arithmetic Addition
Formulas
Compound Interest Formula: A = P(1 + r/n)^(nt)
Total Balance: B(t) = Investment Balance + Savings Balance
Theorems
Properties of Exponential Functions
Suitable Grade Level
Grades 9-11
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