A bank offers 9% per annum simple interest on an investment. At the end of 4 years, the interest earned is $215. How much money (in dollars) was initially invested (principal)?

Introduction:
This question tests finding principal when simple interest, rate, and time are known. Simple interest is SI = (P * r * t)/100. Rearranging gives P = (SI * 100) / (r * t). Because the rate is annual and time is in years, there are no unit conversions needed, making the computation direct. The only care needed is accurate division to get the decimal principal value in dollars.

Given Data / Assumptions:

• Simple interest SI = $215
• Annual rate r = 9% per annum
• Time t = 4 years
• Principal P = ?
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Rearrange the formula to isolate P. Substitute the given values. Since r is in percent, keep r as 9 and use the factor 100 from the formula. The result may be a decimal because interest values in dollars do not have to produce integer principals.

Step-by-Step Solution:
SI = (P * r * t) / 100 P = (SI * 100) / (r * t) P = (215 * 100) / (9 * 4) P = 21500 / 36 P = 597.2222... ≈ 597.22

Verification / Alternative check:
Check: SI = (597.22 * 9 * 4)/100 ≈ 597.22 * 0.36 ≈ 215.0 (difference only due to rounding to 2 decimals). Using the full repeating decimal gives exactly 215.

Why Other Options Are Wrong:
$456 and $378 would yield much smaller interest at 9% over 4 years. $345 is even smaller. $620 would yield interest higher than $215. Only $597.22 matches the required principal based on the formula.

Common Pitfalls:
Forgetting to multiply SI by 100, using 0.09 and still dividing by 100 again, or mixing up amount and interest.

Final Answer:
The initial investment was $597.22 (approximately).