An amount of $720 is invested for 36 months and earns $205.20 in simple interest. What is the corresponding yearly simple interest rate (in percent per annum)?

Introduction / Context:
This question involves calculating the annual simple interest rate when the principal, total interest earned, and time in months are given. It tests your ability to convert months into years and then manipulate the simple interest formula to isolate the rate.

Given Data / Assumptions:

• Principal, P = $720.
• Total simple interest, SI = $205.20.
• Time period, T = 36 months = 3 years.
• Annual simple interest rate, R%, is unknown.

Concept / Approach:
The foundational formula for simple interest is:
SI = (P * R * T) / 100When SI, P, and T are known, we can solve for R using:
R = (SI * 100) / (P * T)The only subtlety here is ensuring that the time is correctly converted from months to years because the rate is given on a per annum basis.

Step-by-Step Solution:
Step 1: Convert time to years.T = 36 months = 36 / 12 = 3 yearsStep 2: Substitute values into the rate formula.R = (SI * 100) / (P * T)R = (205.20 * 100) / (720 * 3)Step 3: Compute the denominator.Denominator = 720 * 3 = 2,160Step 4: Compute the numerator.Numerator = 20,520Step 5: Divide numerator by denominator.R = 20,520 / 2,160 = 9.5Therefore, the annual simple interest rate is 9.5%.

Verification / Alternative check:
We can verify by recomputing the simple interest with R = 9.5%. SI = (720 * 9.5 * 3) / 100. First, 720 * 9.5 = 6,840. Then multiply by 3 to get 20,520, and divide by 100 to get 205.20. This matches the given interest, confirming that the rate is correct.

Why Other Options Are Wrong:

• 7.5%, 8.5%, and 10.5% would each yield interest amounts different from $205.20 when applied for 3 years on $720.
• Only 9.5% reproduces the exact interest of $205.20.

Common Pitfalls:
Candidates sometimes forget to convert 36 months into 3 years correctly or miscalculate the multiplication in the numerator and denominator. It is also common to make errors in decimal placement when dividing 20,520 by 2,160. Carefully setting up the fraction and simplifying step by step helps avoid these mistakes.

Final Answer:
The yearly simple interest rate on the investment is 9.5% per annum.