Question

What is the breakdown of Phyllis's investment amounts given a total investment of $9,500, where a portion earns a simple interest rate of 2 1/5% per year and the remainder earns 2% per year, resulting in a total interest earned of $203 after 1 year?

A) $4,800 at 2 1/5% and $4,700 at 2%
B) $4,700 at 2 1/5% and $4,800 at 2%
C) $5,000 at 2 1/5% and $4,500 at 2%
D) $4,500 at 2 1/5% and $5,000 at 2%

Answer 1

After converting the interest rate 2 1/5% to a decimal (0.022) and setting up the equation, the calculations show $6,500 invested at 2 1/5% and $3,000 at 2%. However, these amounts do not match any of the provided options, suggesting an error in the question or options.

Step-by-step explanation:

To determine Phyllis's investment amounts, we need to allocate the total investment of $9,500 into two parts where one earns a simple interest rate of 2 1/5% per year and the other earns 2% per year for the total interest of $203 earned after 1 year. Let's call the amount invested at 2 1/5% as 'x' and the amount invested at 2% as '$9,500 - x'.

First, we convert the interest rate of 2 1/5% to a decimal, which is 0.022 (2.2/100). Now we can set up the equation for the interest earned from each part:

• x * 0.022 + ($9,500 - x) * 0.02 = $203

Solving this equation:

1. Multiply each term: 0.022x + 190 - 0.02x = 203
2. Combine like terms: 0.002x + 190 = 203
3. Subtract 190 from both sides: 0.002x = 13
4. Divide by 0.002: x = $6,500

Therefore, $6,500 is invested at 2 1/5%, and $9,500 - $6,500 = $3,000 is invested at 2%. However, none of the given options (A, B, C, D) match these calculated amounts, which means there might be a mistake in the question or the provided options.