Jan invests $210 in a fixed deposit account with a building society that pays 8% simple interest per annum for a period of 18 months; how much money in total does she receive at the end of the 18 months?

Introduction / Context:
This question is a direct application of the simple interest formula with time expressed in months rather than years. Jan invests a small amount at a fixed annual rate and the deposit runs for 18 months. The goal is to compute the total amount received, which is the sum of the original principal and the simple interest earned over that period.

Given Data / Assumptions:
- Principal P = 210 dollars. - Annual simple interest rate R = 8 percent per annum. - Time period is 18 months. - Interest is calculated using simple interest, not compound interest. - Required quantity is total amount A = principal + interest.

Concept / Approach:
The simple interest formula SI = (P * R * T) / 100 requires time T in years. Therefore, we first convert 18 months into years. Since 12 months equal 1 year, 18 months equals 18 / 12 = 1.5 years. After converting time, we compute the simple interest, then add it to the principal to obtain the total maturity amount for Jan's deposit.

Step-by-Step Solution:
Step 1: Convert 18 months to years: T = 18 / 12 = 1.5 years. Step 2: Identify P = 210 dollars, R = 8 percent, T = 1.5 years. Step 3: Use SI = (P * R * T) / 100. Step 4: Substitute values: SI = (210 * 8 * 1.5) / 100. Step 5: Compute 210 * 8 = 1,680. Step 6: Multiply 1,680 by 1.5 to get 2,520. Step 7: Divide by 100: SI = 2,520 / 100 = 25.20 dollars. Step 8: Compute total amount A = P + SI = 210 + 25.20 = 235.20 dollars. Step 9: Therefore, Jan receives 235.20 dollars at the end of 18 months.

Verification / Alternative check:
We can think of the annual interest first. For one year, interest is (210 * 8 * 1) / 100 = 16.80 dollars. For half a year (0.5 year), interest is half of that, 8.40 dollars. Summing 16.80 and 8.40 gives 25.20 dollars of total interest in 1.5 years. Adding this to the principal 210 dollars again gives 235.20 dollars, confirming the result.

Why Other Options Are Wrong:
An amount of 434.00 dollars is far larger than possible from such a small principal and rate in only 18 months. An amount of 345.00 dollars also overstates the interest significantly. A total of 233.20 dollars would imply interest of only 23.20 dollars, which does not match the 8 percent rate over 1.5 years. Only 235.20 dollars corresponds to the correct simple interest calculation.

Common Pitfalls:
Learners sometimes forget to convert months to years and instead use T = 18 directly, which hugely overestimates interest. Another mistake is to treat 18 months as 1.8 years instead of 1.5 years. Careful handling of unit conversions for time is crucial when applying interest formulas correctly.

Final Answer:
At the end of 18 months, Jan receives a total of $235.20.