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 does she receive in total at the end of the 18 months?

Introduction / Context:
This question involves calculating simple interest over a fractional number of years, since 18 months is equal to 1.5 years. The key skills tested are converting months to years correctly and then applying the simple interest formula to find the final amount received.

Given Data / Assumptions:

• Principal, P = $210.
• Annual simple interest rate, R = 8% per annum.
• Time period, T = 18 months = 1.5 years.
• Interest is simple, not compounded.

Concept / Approach:
The simple interest formula is:
SI = (P * R * T) / 100Once the simple interest is known, the total amount A that Jan receives is:
A = P + SIIt is crucial to convert the time period from months to years correctly, as the rate given is per annum.

Step-by-Step Solution:
Step 1: Convert the time from months to years.T = 18 months = 18 / 12 = 1.5 yearsStep 2: Apply the simple interest formula.SI = (210 * 8 * 1.5) / 100Step 3: Compute the numerator.210 * 8 = 1,6801,680 * 1.5 = 2,520Step 4: Divide by 100.SI = 2,520 / 100 = $25.20Step 5: Find the total amount.A = P + SI = 210 + 25.20 = $235.20

Verification / Alternative check:
An alternative way is to first find the interest for 1 year, then add half of it for the extra 0.5 year. Interest for 1 year at 8% is (210 * 8) / 100 = $16.80. Interest for 0.5 year is $16.80 / 2 = $8.40. Total interest = 16.80 + 8.40 = $25.20, which leads to the same total amount of $235.20. This confirms the correctness of the calculation.

Why Other Options Are Wrong:

• $434.00 and $345.00 are far too large given the small principal and modest interest rate.
• $233.20 implies an interest of only $23.20, which does not correspond to 8% per annum for 1.5 years.

Common Pitfalls:
A frequent error is to treat 18 months as 18 years or to forget to convert to years at all, leading to massive overestimation of interest. Another common mistake is miscalculating 1.5 as 15 or 0.15. Carefully converting the time and breaking the calculation into manageable steps helps avoid such errors.

Final Answer:
At the end of 18 months, Jan receives a total of $235.20 from her fixed deposit investment.