Question
Carlos has $350 in a savings account that earns 5% simple interest each year. How much will he have in the account after 1 year, if there is no money withdrawn?
- A$17.50
- B$175.00
- C$367.50
- D$525.00
Show the answer
Correct answer: C
Find 5% of 350.
Question analysis
Carlos has $350 in a savings account earning 5% simple interest a year, and this interest question asks how much will be in the account after 1 year with no withdrawals. Students find 5 percent of the balance and use it. Reading whether the question wants the interest or the account's new balance matters most.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Below grade 7 Simple interest is a grade 7 percent topic, but one year of interest is just 5 percent of the balance added on. Typical grade 7 problems run for several years or ask for the rate, so this is lighter.
- Estimated difficulty
- Routine: one familiar step, little to misread.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Solution
- 2 steps
- Reading level
- Question and choices: about grade 6, 28 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
This is a one-year interest question with friendly numbers, so most students who know what interest is will finish it. The two ways to lose the point are stopping at the interest, which is listed, and writing 5% as 0.5, which gives a listed interest and a listed balance of its own. A sensible balance is only a little more than $350, which rules out every wrong choice.
Something you must already know minor Working it out
Simple interest for one year is the rate times the balance, 5% of $350, added to what is already there; the stem does not spell this out. (Anderson & Krathwohl, 2001)
Error-prone arithmetic minor Working it out
Writing 5% as 0.05, not 0.5, is the one place-value decision, and 0.05 × 350 = 17.5 must then be read as $17.50. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Strategy: Find 5 percent of $350 by multiplying by 0.05, then decide whether the question wants the interest alone or the amount in the account.
Traps
- Stops one step early: A choice is a number from partway through the solution.
- An arithmetic slip: The right method with a plausible arithmetic error: a digit, a place value or a times-table fact.
The wrong answers, classified
A Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds the interest, 0.05 × $350 = $17.50, and stops without adding it to the $350 already in the account.
B An arithmetic slip (Junker & Sijtsma, 2001)
Writes 5% as 0.5 instead of 0.05, a decimal slip that makes the interest $175.00, and then also stops at the interest.
D An arithmetic slip (Junker & Sijtsma, 2001)
Writes 5% as 0.5, so the interest comes out as $175.00, and adds it to the $350 to reach $525.00.
Worked solution, step by step
Formulas used
- Simple interest
- I is the interest, the extra money the bank pays you. P is the principal, the money you put in. r is the yearly rate as a decimal. t is the time in years. Simple means you earn interest only on the money you started with.
Sort out the question
Carlos starts with $350. The account earns 5% simple interest each year. Interest is extra money the bank adds to your account. You need the total in the account after 1 year. That is the $350 plus the interest.
Change the percent to a decimal
Percent means out of 100, so 5% is 5 out of 100.
Watch out: 5% is 0.05, not 0.5. Using 0.5 makes the interest $175, which leads to B or D.Find the interest
Put in P = 350, r = 0.05 and t = 1 year.
The interest for one year is $17.50. That is the money added to the account.
Add the interest to the savings
After 1 year, Carlos has $367.50. Watch out: $17.50 is only the interest, choice A. The question asks how much is in the account.
So the answer is C, $367.50.
Check your answer
10% of $350 is $35. 5% is half of that, $17.50, so the interest is right. The total should be a little more than $350, since 5% is small. $367.50 fits. $525.00 would mean the account grew by half.
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