Grade 7 · Ratios & Proportional Reasoning · MAT-07-RP-008
Solve Simple Interest Problems
Represent and solve solve simple interest problems problems using precise mathematical notation, models, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve solve simple interest problems problems using precise mathematical notation, models, and reasoning.
- Explain why a method for solve simple interest problems works, interpret the result in context, and verify it independently.
Prerequisite check
Make sure the foundation is ready.
The new lesson depends on this prerequisite as active knowledge.
Learn
Build the idea from meaning, not memorization.
Mathematical meaning
Solve Simple Interest Problems is about multiplicative comparison. Equivalent representations preserve the same scale relationship, not merely the same difference.
Represent the relationship
The Math Box uses percent model to expose the structure. Change one input, predict the result, then connect the visual change to an equation, table, graph, number line, or geometric model.
Calculate, interpret, and verify
Verify with an inverse operation, equivalent representation, estimate, or second method so both the calculation and reasoning are auditable.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Percent Lab
Percent means “per 100.” Change the percent and the whole to see the part update.
- Model one example of solve simple interest problems in the Math Box.
- Change one input, predict the effect, and test the prediction.
- State the relationship or invariant that explains what stayed mathematically consistent.
Worked examples
Twenty different ways to see the concept work.
Find simple interest on $100 at 3% for 1 years.
I = Prt = 100 × 0.03 × 1 = 3Simple interest uses the original principal for every time period.
Find simple interest on $125 at 4% for 2 years.
I = Prt = 125 × 0.04 × 2 = 10Simple interest uses the original principal for every time period.
Find simple interest on $150 at 5% for 3 years.
I = Prt = 150 × 0.05 × 3 = 22.5Simple interest uses the original principal for every time period.
Find simple interest on $175 at 6% for 4 years.
I = Prt = 175 × 0.06 × 4 = 42Simple interest uses the original principal for every time period.
Find simple interest on $200 at 3% for 5 years.
I = Prt = 200 × 0.03 × 5 = 30Simple interest uses the original principal for every time period.
Find simple interest on $225 at 4% for 1 years.
I = Prt = 225 × 0.04 × 1 = 9Simple interest uses the original principal for every time period.
Find simple interest on $250 at 5% for 2 years.
I = Prt = 250 × 0.05 × 2 = 25Simple interest uses the original principal for every time period.
Find simple interest on $275 at 6% for 3 years.
I = Prt = 275 × 0.06 × 3 = 49.5Simple interest uses the original principal for every time period.
Find simple interest on $300 at 3% for 4 years.
I = Prt = 300 × 0.03 × 4 = 36Simple interest uses the original principal for every time period.
Find simple interest on $325 at 4% for 5 years.
I = Prt = 325 × 0.04 × 5 = 65Simple interest uses the original principal for every time period.
Find simple interest on $350 at 5% for 1 years.
I = Prt = 350 × 0.05 × 1 = 17.5Simple interest uses the original principal for every time period.
Find simple interest on $375 at 6% for 2 years.
I = Prt = 375 × 0.06 × 2 = 45Simple interest uses the original principal for every time period.
Find simple interest on $400 at 3% for 3 years.
I = Prt = 400 × 0.03 × 3 = 36Simple interest uses the original principal for every time period.
Find simple interest on $425 at 4% for 4 years.
I = Prt = 425 × 0.04 × 4 = 68Simple interest uses the original principal for every time period.
Find simple interest on $450 at 5% for 5 years.
I = Prt = 450 × 0.05 × 5 = 112.5Simple interest uses the original principal for every time period.
Find simple interest on $475 at 6% for 1 years.
I = Prt = 475 × 0.06 × 1 = 28.5Simple interest uses the original principal for every time period.
Find simple interest on $500 at 3% for 2 years.
I = Prt = 500 × 0.03 × 2 = 30Simple interest uses the original principal for every time period.
Find simple interest on $525 at 4% for 3 years.
I = Prt = 525 × 0.04 × 3 = 63Simple interest uses the original principal for every time period.
Find simple interest on $550 at 5% for 4 years.
I = Prt = 550 × 0.05 × 4 = 110Simple interest uses the original principal for every time period.
Find simple interest on $575 at 6% for 5 years.
I = Prt = 575 × 0.06 × 5 = 172.5Simple interest uses the original principal for every time period.
Practice
Guided practice with hints
01Find simple interest on $600 at 3% for 1 years.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: I = Prt = 600 × 0.03 × 1 = 18
02Find simple interest on $625 at 4% for 2 years.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: I = Prt = 625 × 0.04 × 2 = 50
03Find simple interest on $650 at 5% for 3 years.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: I = Prt = 650 × 0.05 × 3 = 97.5
04Find simple interest on $675 at 6% for 4 years.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: I = Prt = 675 × 0.06 × 4 = 162
05Find simple interest on $700 at 3% for 5 years.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: I = Prt = 700 × 0.03 × 5 = 105
06Find simple interest on $725 at 4% for 1 years.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: I = Prt = 725 × 0.04 × 1 = 29
Practice
Independent practice
01Find simple interest on $750 at 5% for 2 years.
Answer: I = Prt = 750 × 0.05 × 2 = 75
02Find simple interest on $775 at 6% for 3 years.
Answer: I = Prt = 775 × 0.06 × 3 = 139.5
03Find simple interest on $800 at 3% for 4 years.
Answer: I = Prt = 800 × 0.03 × 4 = 96
04Find simple interest on $825 at 4% for 5 years.
Answer: I = Prt = 825 × 0.04 × 5 = 165
05Find simple interest on $850 at 5% for 1 years.
Answer: I = Prt = 850 × 0.05 × 1 = 42.5
06Find simple interest on $875 at 6% for 2 years.
Answer: I = Prt = 875 × 0.06 × 2 = 105
07Find simple interest on $900 at 3% for 3 years.
Answer: I = Prt = 900 × 0.03 × 3 = 81
08Find simple interest on $925 at 4% for 4 years.
Answer: I = Prt = 925 × 0.04 × 4 = 148
Common mistakes
Learn to catch the error, not just the answer.
Check for a common scale factor or constant unit rate.
Convert both to a common unit rate first.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Compare prices, speeds, recipes, maps, taxes, discounts, tips, and rates using common units.
- Scale designs and predict related quantities while preserving multiplicative relationships.
Challenge problems
Find simple interest on $950 at 5% for 5 years.
I = Prt = 950 × 0.05 × 5 = 237.5
Find simple interest on $975 at 6% for 1 years.
I = Prt = 975 × 0.06 × 1 = 58.5
Find simple interest on $1000 at 3% for 2 years.
I = Prt = 1000 × 0.03 × 2 = 60
Find simple interest on $1025 at 4% for 3 years.
I = Prt = 1025 × 0.04 × 3 = 123
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 7 Reasoning Sprint
Solve solve simple interest problems problems accurately and justify each result with a valid check.
Practice
Mastery check
01Find simple interest on $1050 at 5% for 4 years.
Answer: I = Prt = 1050 × 0.05 × 4 = 210
02Find simple interest on $1075 at 6% for 5 years.
Answer: I = Prt = 1075 × 0.06 × 5 = 322.5
03Find simple interest on $1100 at 3% for 1 years.
Answer: I = Prt = 1100 × 0.03 × 1 = 33
04Find simple interest on $1125 at 4% for 2 years.
Answer: I = Prt = 1125 × 0.04 × 2 = 90
05Find simple interest on $1150 at 5% for 3 years.
Answer: I = Prt = 1150 × 0.05 × 3 = 172.5
06Find simple interest on $1175 at 6% for 4 years.
Answer: I = Prt = 1175 × 0.06 × 4 = 282
07Find simple interest on $1200 at 3% for 5 years.
Answer: I = Prt = 1200 × 0.03 × 5 = 180
08Find simple interest on $1225 at 4% for 1 years.
Answer: I = Prt = 1225 × 0.04 × 1 = 49
Terminology
Words to know
- ratio
- A multiplicative comparison between two quantities.
- unit rate
- A rate expressed per one unit of the second quantity.
- equivalent ratios
- Ratios made by scaling both quantities by the same nonzero factor.
- constant of proportionality
- The unit rate k in a proportional equation y = kx.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Middle-school instructional guidance, mathematical practices, modeling, and coherent progression.Common Core State Standards for Mathematics — Grade 7
Grade-level expectations for ratios, number systems, algebra, geometry, statistics, and probability.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.