An investment of $150 grows to $186 after one year with simple interest. What is the annual interest rate as...

1. TRANSLATE the problem information

• Given information:
  • Principal (initial investment): \(\$150\)
  • Final amount after 1 year: \(\$186\)
  • Need to find: annual interest rate as a percentage

2. INFER what we need to calculate first

• To find the interest rate, we first need to determine how much interest was earned
• Interest earned = Final amount - Principal

3. Calculate the interest earned

• Interest = \(\$186 - \$150 = \$36\)

4. INFER which formula to use

• For simple interest: \(\mathrm{Interest} = \mathrm{Principal} \times \mathrm{Rate} \times \mathrm{Time}\)
• Since time = 1 year, we can rearrange to: \(\mathrm{Rate} = \mathrm{Interest} \div \mathrm{Principal}\)

5. SIMPLIFY to find the rate

• Rate = \(\$36 \div \$150 = 0.24\)
• Convert to percentage: \(0.24 \times 100\% = 24\%\)

Answer: 24

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students try to work directly with the given amounts without recognizing they need to find the interest earned first.

They might attempt calculations like \(\$186 \div \$150 = 1.24\), then get confused about what this represents, leading to answers like 124% or getting stuck and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify the interest as \(\$36\) but make arithmetic errors in the division or forget to convert the decimal to a percentage.

This might lead them to answers like 2.4 (forgetting to multiply by 100) or calculation errors that produce incorrect decimal values.

The Bottom Line:

This problem requires recognizing that simple interest problems involve a two-step process: first calculate the interest earned, then apply the rate formula. Students who jump straight to using the given numbers often miss this crucial insight.