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?

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

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:

\[0.05x + 0.08(10,\!000 - x) = 680\]

Solving for \( x \)

Start by expanding the equation:

\[0.05x + 800 - 0.08x = 680\]

Combine like terms:

\[-0.03x + 800 = 680\]

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.

Whether you're a beginner or a seasoned investor, mastering such calculations strengthens your financial literacy and investment confidence.