An initial deposit of $1,200 is made into an account that earns simple interest at an annual rate of 4.5%....

1. TRANSLATE the problem information

• Given information:
  • Principal amount: $1,200
  • Annual interest rate: 4.5%
  • Time period: 1 year
  • Need to find: Amount of interest earned

2. INFER the approach

• This is a simple interest problem (not compound interest)
• We need the simple interest formula: \(\mathrm{I = Prt}\)
• We're looking for just the interest amount, not the total balance

3. TRANSLATE the rate to decimal form

• Convert 4.5% to decimal: \(\mathrm{4.5 \div 100 = 0.045}\) (use calculator if needed)
• This step is crucial - percentages must be decimals in formulas

4. INFER and substitute into the formula

• \(\mathrm{I = Prt}\) becomes \(\mathrm{I = 1200 \times 0.045 \times 1}\)
• Since \(\mathrm{t = 1}\) year, this simplifies to: \(\mathrm{I = 1200(0.045)}\)
• This expression gives us exactly what we need

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students use 4.5 directly instead of converting to 0.045

They might think "4.5% means 4.5" and calculate \(\mathrm{1200 \times 4.5}\), leading them to look for an expression with 4.5 rather than 0.045. Since none of the choices contain 4.5, this leads to confusion and guessing.

Second Most Common Error:

Poor INFER reasoning: Students confuse simple interest with final balance calculation

They think they need the total amount in the account after one year, so they look for \(\mathrm{1200(1.045)}\), which represents the principal plus interest. This may lead them to select Choice D \(\mathrm{(1200(1.045))}\).

The Bottom Line:

This problem tests whether students can distinguish between "interest earned" versus "total balance" and whether they can properly convert percentages to decimals for use in formulas.