An effective annual interest rate is the real return on a savings account or any interest-paying investment when the effects of compounding are taken into account. It is important to consider this rate when allocating investments in order to maximize interest earnings. By strategically dividing your investment between two accounts with different interest rates, you can optimize your returns.

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To determine how much should be invested at each interest rate, consider the total interest earned for the year. Let's assume the total interest earned is $X. By allocating a certain amount, denoted as $Y, into an account with an interest rate of A%, and the remaining amount, denoted as $Z, into an account with an interest rate of B%, we can solve for Y and Z.

The formula for calculating interest earned is: Interest Earned = (Principal × Rate × Time). Using this formula, we can set up two equations. The first equation is: Y × (A/100) = (Y × A/100) × 1. The second equation is: Z × (B/100) = (Z × B/100) × 1.

Simplifying these equations, we find that Y = X × (B/100) / (A/100 + B/100) and Z = X × (A/100) / (A/100 + B/100). These formulas allow us to determine the optimal allocation of investments to maximize interest earnings.

To illustrate this concept, let's consider an example. Suppose you have $10,000 to invest, and you want to allocate it between two accounts with interest rates of 5% and 7% respectively. Using the formulas mentioned earlier, we find that $4,000 should be invested in the 5% account, while $6,000 should be invested in the 7% account. This allocation will yield the maximum interest earnings.

It is important to note that the allocation strategy may vary depending on the specific interest rates and investment options available. Additionally, risk tolerance and investment goals should also be considered when determining the allocation of investments.

In conclusion, by strategically allocating investments between accounts with different interest rates, you can maximize your annual interest earnings. Utilizing the formulas provided, you can determine the optimal allocation of investments based on the total interest earned for the year. Keep in mind that individual circumstances and goals may influence the allocation strategy. Remember to regularly review and adjust your investment allocations to ensure optimal returns over time.