Optimizing Investment Returns with Bank A and Bank B

How can Peter maximize his investment returns by placing money in Bank A and Bank B?

Given that Peter has $24,000 to invest, how much should he deposit in each bank to earn the highest return on his investment?

Final Answer:

Peter deposited $9,200 in Bank A and $14,800 in Bank B.

Suppose Peter has $24,000 to invest and decides to place part of it in Bank A at an interest rate of 6% per year, while the remaining part is placed in Bank B at 5.5% per year. If Peter earns $1,412.50 in one year, the optimal deposit amounts are calculated as follows:

Let's denote the amount Peter deposited in Bank A as x dollars and the remaining amount (24,000 - x) in Bank B. The interest earned from Bank A after one year is 0.06x, and from Bank B is 0.055(24,000 - x).

Setting up the equation to find the optimal deposit amounts:

Solving for x:

Therefore, Peter should deposit $9,200 in Bank A and $14,800 in Bank B to maximize his investment returns.