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

Introduction:
This question tests finding time in a simple interest situation. Under simple interest, interest accumulates at a constant amount each year: yearly interest = (P * r)/100. Since the interest is paid out annually and does not compound, we can either use the standard formula SI = (P * r * t)/100 or compute yearly interest and divide the required total interest by that yearly amount.

Given Data / Assumptions:

• Principal P = $750
• Annual simple interest rate r = 4% per annum
• Total simple interest needed SI = $150
• Time = t years (unknown)
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Rearrange the simple interest formula to solve for time: t = (SI * 100) / (P * r). Alternatively, compute interest per year and then compute how many years are needed to reach $150. Both methods should agree because simple interest is linear in time.

Step-by-Step Solution:
SI = (P * r * t) / 100 t = (SI * 100) / (P * r) t = (150 * 100) / (750 * 4) t = 15000 / 3000 t = 5

Verification / Alternative check:
Yearly interest = 4% of 750 = 0.04 * 750 = $30 per year. To earn $150, years = 150 / 30 = 5 years. This matches the formula result.

Why Other Options Are Wrong:
4 years gives only $120 (4 * 30). 6, 7, and 8 years give $180, $210, and $240 respectively, which exceed $150. Only 5 years produces exactly $150 in simple interest.

Common Pitfalls:
Accidentally compounding interest, using 4 as 0.4, forgetting to divide by 100, or thinking the principal changes because interest is paid out (principal remains $750 in a simple interest setup).

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