A savings account starts with a balance of $1,800 and earns $40 in interest each month. Based on this interest...

1. TRANSLATE the problem information

• Given information:
  • Starting balance: \(\$1,800\)
  • Monthly interest earned: \(\$40\)
  • Target balance: \(\$3,400\)
• What we need to find: Number of months to reach the target

2. INFER the approach

• To solve this, we need to find how much the account must grow, then determine how many months of \(\$40\) interest it takes to achieve that growth
• Strategy: Find the difference between target and starting balance, then divide by monthly interest

3. SIMPLIFY by calculating the required increase

• Required increase = \(\$3,400 - \$1,800 = \$1,600\)
• The account needs to grow by exactly \(\$1,600\)

4. SIMPLIFY by finding the number of months needed

• Number of months = Total increase needed ÷ Monthly interest
• Number of months = \(\$1,600 ÷ \$40 = 40\text{ months}\)

Answer: B (40 months)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret what value to use in their calculation, often dividing the starting balance by the monthly interest instead of finding the increase first.

They calculate: \(\$1,800 ÷ \$40 = 45\text{ months}\), thinking "how long will it take to earn the starting balance in interest?"

This may lead them to select Choice C (45).

Second Most Common Error:

Poor INFER reasoning: Students recognize they need to divide something by \(\$40\), but they divide the target balance directly without subtracting the starting amount.

They calculate: \(\$3,400 ÷ \$40 = 85\text{ months}\), but since 85 isn't among the choices, this leads to confusion and guessing, possibly selecting Choice D (80) as the closest option.

The Bottom Line:

This problem requires careful attention to what the question is actually asking. The key insight is recognizing that you only need to earn enough interest to cover the increase from starting balance to target balance, not the entire target amount.