Problem
Interest rate is interest over principal
A bank pays a known amount of interest on a known deposit in one year. We need the total that can be withdrawn after a year on a larger deposit.
Ratios
Your answer
How to solve
Strategy Analyze the Units — Find the rate once and it applies to any deposit. Then remember what is being asked -- the withdrawal is the deposit plus the interest, not the interest on its own.
1STEP 1
Find the interest rate
The rate is the interest divided by the money deposited.
9200 ÷ 400000 = 0.023
The rate is 0.023, or 2.3%.
6.RP.A.3Analyze The Units2STEP 2
Apply it to the larger deposit
The same rate applies, so multiply Sua's deposit by it.
600000 × 0.023 = 13800
Sua earns 13,800 won in interest.
7.RP.A.3Organize Information In More WaysThe same rate applies to the larger deposit.
Why?
The bank pays a fixed amount of interest for each won deposited, so a deposit is that many equal payments and a bigger deposit is simply more of them.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
3STEP 3
Add the interest to the deposit
What she withdraws is her own money back plus what it earned.
600000 + 13800 = 613800
She withdraws 613,800 won.
7.RP.A.3Identify SubproblemsAnswer
613,800 won
Check by scaling instead: 600,000 is one and a half times 400,000, and 9200 × 1.5 = 13800 -- the same interest without ever finding the rate.
Takeaway
Find the rate once and it fits any amount -- but read carefully whether the question wants the interest or the total.
- Find the interest rate
- Apply it to the larger deposit
- Add the interest to the deposit