An investor splits $10,000 between two accounts. One account earns 5% annual interest, and the other earns 8%. If the total interest earned after one year is $680, how much is invested in each account? - Noxie
How an Investor Split $10,000 to Earn $680 in One Year: The Math Behind the Interest Breakdown
How an Investor Split $10,000 to Earn $680 in One Year: The Math Behind the Interest Breakdown
When managing investments, understanding how to allocate your capital strategically can significantly impact your returns. A common question investors face is how to split funds between two accounts earning different annual interest rates. A classic real-world example involves balancing moderate returns (5%) and higher-yield accounts (8%) to achieve a targeted income. In this case, we explore how an investor split $10,000 between two accounts—earning 5% and 8%—to generate exactly $680 in annual interest.
The Investment Split Explained
Understanding the Context
Let’s define the variables clearly:
Let \( x \) be the amount invested at 5% annual interest.
Then, \( 10,\!000 - x \) is invested at 8% annual interest.
The interest earned from each account is calculated as:
- Interest from 5% account: \( 0.05x \)
- Interest from 8% account: \( 0.08(10,\!000 - x) \)
According to the problem, the total interest earned after one year is $680:
\[
0.05x + 0.08(10,\!000 - x) = 680
\]
Image Gallery
Key Insights
Solving for \( x \)
Start by expanding the equation:
\[
0.05x + 800 - 0.08x = 680
\]
Combine like terms:
\[
-0.03x + 800 = 680
\]
🔗 Related Articles You Might Like:
The Silent Honk That Shook Every Neighbor on Friday Night Friday Night Honking That Made the Whole Town Scream—For All the Wrong Reasons You’re Not Ready for What Rumors Sparked at Friday Night HonkingFinal Thoughts
Subtract 800 from both sides:
\[
-0.03x = -120
\]
Divide by -0.03:
\[
x = \frac{-120}{-0.03} = 4,\!000
\]
So, $4,000 is invested at 5%, and the remainder — $10,000 – $4,000 = $6,000 — is invested at 8%.
Verification
Calculate interest from each account:
- 5% of $4,000 = \( 0.05 \ imes 4,\!000 = 200 \)
- 8% of $6,000 = \( 0.08 \ imes 6,\!000 = 480 \)
Total interest = \( 200 + 480 = 680 \), confirming the solution.
Conclusion
This scenario demonstrates a practical investment strategy: splitting funds between a conservative 5% account and a higher-yield 8% account to meet a precise financial goal. By applying basic algebra, the investor efficiently determined that $4,000 should go into the lower-yield account and $6,000 into the 8% account. Understanding this approach empowers investors to make informed decisions when balancing returns, risk, and time in their portfolio planning.
Key Takeaways:
- Use algebraic equations to model investment allocation problems.
- Splitting funds strategically between fixed-income accounts optimizes returns.
- Always verify your calculation to ensure accurate financial outcomes.
