You invest $750 into a certificate of deposit at a simple annual interest rate of 4%. You receive a check for the interest at the end of each year. How many years will it take to earn a total of $150 in simple interest?

Introduction / Context:
This simple interest question asks for the time required to earn a specific total amount of interest, given the principal and the annual rate. The interest is paid out each year, but the calculation still follows the standard simple interest formula.

Given Data / Assumptions:

• Principal (P) = $750.
• Rate of interest (R) = 4% per annum.
• Total simple interest desired (SI) = $150.
• Time in years (T) is unknown.
• Interest is simple, not compounded, and the principal does not change over time.

Concept / Approach:
For simple interest, SI = (P * R * T) / 100. When you know SI, P, and R, you can rearrange the formula to find T as T = (SI * 100) / (P * R). Then substitute the given values and compute the required number of years.

Step-by-Step Solution:
Step 1: Use the simple interest formula: SI = (P * R * T) / 100. Step 2: Rearrange to solve for T: T = (SI * 100) / (P * R). Step 3: Substitute SI = 150, P = 750, and R = 4. Step 4: T = (150 * 100) / (750 * 4). Step 5: Compute the denominator: 750 * 4 = 3000. Step 6: Compute the numerator: 150 * 100 = 15000. Step 7: T = 15000 / 3000 = 5 years.

Verification / Alternative check:
You can think of the yearly interest as 4% of 750, which is (750 * 4) / 100 = 30 per year. To earn $150 in total interest at this rate, you need 150 / 30 = 5 years, which matches the result from the formula.

Why Other Options Are Wrong:
6, 7, and 8 years would produce total interest of 180, 210, and 240 respectively at $30 per year, which are all greater than the target of $150.

Common Pitfalls:
Some students confuse simple interest with compound interest and unnecessarily complicate the problem. Others miscalculate the number of years by skipping the step of finding yearly interest. Recognizing that, under simple interest, the interest grows linearly with time makes the problem straightforward.

Final Answer:
It will take 5years to earn a total of $150 in simple interest.