Practice · Interest is a rate on the principal, and the principal comes back too · Sensim Math

Variant 1 easy

Depositing $250{,}000$ won in a bank for one year earns $2500$ won in interest. If Sua deposits $300{,}000$ won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Your answer

Show solution

1 · Understandwhat's really being asked

250,000 won earns 2,500 won of interest in a year. Sua puts in 300,000 won at the same rate, and we want everything she can take out after a year.

Givens

250,000 won earns 2,500 won in one year.
Sua deposits 300,000 won.
The rate is the same for both deposits.

Unknowns

The total Sua can withdraw after one year.

Constraints

Interest is proportional to the amount deposited.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3

Divide the interest by the deposit it came from.

2,500 \div 250{,}000 = 0.01 = 1\%

The bank pays 1 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3

The same rate on 300,000 won.

300{,}000 \times 0.01 = 3{,}000

She earns 3,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3

Withdrawing in all means her own money plus what it earned.

300{,}000 + 3{,}000 = 303{,}000

303,000 won in total.

Answer: 303,000 won

4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.01 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio $300{,}000 : 250{,}000$ skips the percentage and lands on the same 3,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.

💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.

Variant 2 easy

Depositing $100{,}000$ won in a bank for one year earns $3000$ won in interest. If Sua deposits $350{,}000$ won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Your answer

Show solution

1 · Understandwhat's really being asked

100,000 won earns 3,000 won of interest in a year. Sua puts in 350,000 won at the same rate, and we want everything she can take out after a year.

Givens

100,000 won earns 3,000 won in one year.
Sua deposits 350,000 won.
The rate is the same for both deposits.

Unknowns

The total Sua can withdraw after one year.

Constraints

Interest is proportional to the amount deposited.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3

Divide the interest by the deposit it came from.

3,000 \div 100{,}000 = 0.03 = 3\%

The bank pays 3 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3

The same rate on 350,000 won.

350{,}000 \times 0.03 = 10{,}500

She earns 10,500 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3

Withdrawing in all means her own money plus what it earned.

350{,}000 + 10{,}500 = 360{,}500

360,500 won in total.

Answer: 360,500 won

4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.03 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio $350{,}000 : 100{,}000$ skips the percentage and lands on the same 10,500 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.

💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.

Variant 3 easy

Depositing $150{,}000$ won in a bank for one year earns $3750$ won in interest. If Sua deposits $600{,}000$ won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Your answer

Show solution

1 · Understandwhat's really being asked

150,000 won earns 3,750 won of interest in a year. Sua puts in 600,000 won at the same rate, and we want everything she can take out after a year.

Givens

150,000 won earns 3,750 won in one year.
Sua deposits 600,000 won.
The rate is the same for both deposits.

Unknowns

The total Sua can withdraw after one year.

Constraints

Interest is proportional to the amount deposited.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3

Divide the interest by the deposit it came from.

3,750 \div 150{,}000 = 0.025 = 2.5\%

The bank pays 2.5 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3

The same rate on 600,000 won.

600{,}000 \times 0.025 = 15{,}000

She earns 15,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3

Withdrawing in all means her own money plus what it earned.

600{,}000 + 15{,}000 = 615{,}000

615,000 won in total.

Answer: 615,000 won

4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.025 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio $600{,}000 : 150{,}000$ skips the percentage and lands on the same 15,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.

💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.

Variant 4 easy

Depositing $350{,}000$ won in a bank for one year earns $7000$ won in interest. If Sua deposits $850{,}000$ won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Your answer

Show solution

1 · Understandwhat's really being asked

350,000 won earns 7,000 won of interest in a year. Sua puts in 850,000 won at the same rate, and we want everything she can take out after a year.

Givens

350,000 won earns 7,000 won in one year.
Sua deposits 850,000 won.
The rate is the same for both deposits.

Unknowns

The total Sua can withdraw after one year.

Constraints

Interest is proportional to the amount deposited.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3

Divide the interest by the deposit it came from.

7,000 \div 350{,}000 = 0.02 = 2\%

The bank pays 2 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3

The same rate on 850,000 won.

850{,}000 \times 0.02 = 17{,}000

She earns 17,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3

Withdrawing in all means her own money plus what it earned.

850{,}000 + 17{,}000 = 867{,}000

867,000 won in total.

Answer: 867,000 won

4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.02 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio $850{,}000 : 350{,}000$ skips the percentage and lands on the same 17,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.

💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.

Variant 5 medium

Depositing $600{,}000$ won in a bank for one year earns $9000$ won in interest. If Sua deposits $350{,}000$ won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Your answer

Show solution

1 · Understandwhat's really being asked

600,000 won earns 9,000 won of interest in a year. Sua puts in 350,000 won at the same rate, and we want everything she can take out after a year.

Givens

600,000 won earns 9,000 won in one year.
Sua deposits 350,000 won.
The rate is the same for both deposits.

Unknowns

The total Sua can withdraw after one year.

Constraints

Interest is proportional to the amount deposited.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3

Divide the interest by the deposit it came from.

9,000 \div 600{,}000 = 0.015 = 1.5\%

The bank pays 1.5 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3

The same rate on 350,000 won.

350{,}000 \times 0.015 = 5{,}250

She earns 5,250 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3

Withdrawing in all means her own money plus what it earned.

350{,}000 + 5{,}250 = 355{,}250

355,250 won in total.

Answer: 355,250 won

4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.015 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio $350{,}000 : 600{,}000$ skips the percentage and lands on the same 5,250 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.

💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.

Variant 6 medium

Depositing $400{,}000$ won in a bank for one year earns $9200$ won in interest. If Sua deposits $600{,}000$ won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Your answer

Show solution

1 · Understandwhat's really being asked

400,000 won earns 9,200 won of interest in a year. Sua puts in 600,000 won at the same rate, and we want everything she can take out after a year.

Givens

400,000 won earns 9,200 won in one year.
Sua deposits 600,000 won.
The rate is the same for both deposits.

Unknowns

The total Sua can withdraw after one year.

Constraints

Interest is proportional to the amount deposited.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3

Divide the interest by the deposit it came from.

9,200 \div 400{,}000 = 0.023 = 2.3\%

The bank pays 2.3 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3

The same rate on 600,000 won.

600{,}000 \times 0.023 = 13{,}800

She earns 13,800 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3

Withdrawing in all means her own money plus what it earned.

600{,}000 + 13{,}800 = 613{,}800

613,800 won in total.

Answer: 613,800 won

4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.023 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio $600{,}000 : 400{,}000$ skips the percentage and lands on the same 13,800 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.

💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.

Variant 7 medium

Depositing $500{,}000$ won in a bank for one year earns $10000$ won in interest. If Sua deposits $900{,}000$ won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Your answer

Show solution

1 · Understandwhat's really being asked

500,000 won earns 10,000 won of interest in a year. Sua puts in 900,000 won at the same rate, and we want everything she can take out after a year.

Givens

500,000 won earns 10,000 won in one year.
Sua deposits 900,000 won.
The rate is the same for both deposits.

Unknowns

The total Sua can withdraw after one year.

Constraints

Interest is proportional to the amount deposited.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3

Divide the interest by the deposit it came from.

10,000 \div 500{,}000 = 0.02 = 2\%

The bank pays 2 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3

The same rate on 900,000 won.

900{,}000 \times 0.02 = 18{,}000

She earns 18,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3

Withdrawing in all means her own money plus what it earned.

900{,}000 + 18{,}000 = 918{,}000

918,000 won in total.

Answer: 918,000 won

4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.02 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio $900{,}000 : 500{,}000$ skips the percentage and lands on the same 18,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.

💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.

Variant 8 medium

Depositing $450{,}000$ won in a bank for one year earns $10350$ won in interest. If Sua deposits $800{,}000$ won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Your answer

Show solution

1 · Understandwhat's really being asked

450,000 won earns 10,350 won of interest in a year. Sua puts in 800,000 won at the same rate, and we want everything she can take out after a year.

Givens

450,000 won earns 10,350 won in one year.
Sua deposits 800,000 won.
The rate is the same for both deposits.

Unknowns

The total Sua can withdraw after one year.

Constraints

Interest is proportional to the amount deposited.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3

Divide the interest by the deposit it came from.

10,350 \div 450{,}000 = 0.023 = 2.3\%

The bank pays 2.3 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3

The same rate on 800,000 won.

800{,}000 \times 0.023 = 18{,}400

She earns 18,400 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3

Withdrawing in all means her own money plus what it earned.

800{,}000 + 18{,}400 = 818{,}400

818,400 won in total.

Answer: 818,400 won

4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.023 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio $800{,}000 : 450{,}000$ skips the percentage and lands on the same 18,400 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.

💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.

Variant 9 hard

Depositing $750{,}000$ won in a bank for one year earns $15000$ won in interest. If Sua deposits $100{,}000$ won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Your answer

Show solution

1 · Understandwhat's really being asked

750,000 won earns 15,000 won of interest in a year. Sua puts in 100,000 won at the same rate, and we want everything she can take out after a year.

Givens

750,000 won earns 15,000 won in one year.
Sua deposits 100,000 won.
The rate is the same for both deposits.

Unknowns

The total Sua can withdraw after one year.

Constraints

Interest is proportional to the amount deposited.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3

Divide the interest by the deposit it came from.

15,000 \div 750{,}000 = 0.02 = 2\%

The bank pays 2 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3

The same rate on 100,000 won.

100{,}000 \times 0.02 = 2{,}000

She earns 2,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3

Withdrawing in all means her own money plus what it earned.

100{,}000 + 2{,}000 = 102{,}000

102,000 won in total.

Answer: 102,000 won

4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.02 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio $100{,}000 : 750{,}000$ skips the percentage and lands on the same 2,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.

💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.

Variant 10 hard

Depositing $900{,}000$ won in a bank for one year earns $18000$ won in interest. If Sua deposits $350{,}000$ won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Your answer

Show solution

1 · Understandwhat's really being asked

900,000 won earns 18,000 won of interest in a year. Sua puts in 350,000 won at the same rate, and we want everything she can take out after a year.

Givens

900,000 won earns 18,000 won in one year.
Sua deposits 350,000 won.
The rate is the same for both deposits.

Unknowns

The total Sua can withdraw after one year.

Constraints

Interest is proportional to the amount deposited.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3

Divide the interest by the deposit it came from.

18,000 \div 900{,}000 = 0.02 = 2\%

The bank pays 2 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3

The same rate on 350,000 won.

350{,}000 \times 0.02 = 7{,}000

She earns 7,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3

Withdrawing in all means her own money plus what it earned.

350{,}000 + 7{,}000 = 357{,}000

357,000 won in total.

Answer: 357,000 won

4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.02 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio $350{,}000 : 900{,}000$ skips the percentage and lands on the same 7,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.

💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.

Variant 11 hard

Depositing $900{,}000$ won in a bank for one year earns $27000$ won in interest. If Sua deposits $650{,}000$ won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Your answer

Show solution

1 · Understandwhat's really being asked

900,000 won earns 27,000 won of interest in a year. Sua puts in 650,000 won at the same rate, and we want everything she can take out after a year.

Givens

900,000 won earns 27,000 won in one year.
Sua deposits 650,000 won.
The rate is the same for both deposits.

Unknowns

The total Sua can withdraw after one year.

Constraints

Interest is proportional to the amount deposited.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3

Divide the interest by the deposit it came from.

27,000 \div 900{,}000 = 0.03 = 3\%

The bank pays 3 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3

The same rate on 650,000 won.

650{,}000 \times 0.03 = 19{,}500

She earns 19,500 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3

Withdrawing in all means her own money plus what it earned.

650{,}000 + 19{,}500 = 669{,}500

669,500 won in total.

Answer: 669,500 won

4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.03 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio $650{,}000 : 900{,}000$ skips the percentage and lands on the same 19,500 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.

💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.

Variant 12 hard

Depositing $700{,}000$ won in a bank for one year earns $28000$ won in interest. If Sua deposits $600{,}000$ won in the same bank, how much can she withdraw after one year in all? (The bank's interest rate stays the same.)

Your answer

Show solution

1 · Understandwhat's really being asked

700,000 won earns 28,000 won of interest in a year. Sua puts in 600,000 won at the same rate, and we want everything she can take out after a year.

Givens

700,000 won earns 28,000 won in one year.
Sua deposits 600,000 won.
The rate is the same for both deposits.

Unknowns

The total Sua can withdraw after one year.

Constraints

Interest is proportional to the amount deposited.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#13 Convert to Algebra

The first deposit is not there to be compared with the second -- it is there to give the rate. Find the rate, apply it to Sua's deposit, and then remember she gets her deposit back as well.

3 · Execute3 carry out the plan

1Find the interest rate

#8 Analyze the Units 6.RP.A.3

Divide the interest by the deposit it came from.

28,000 \div 700{,}000 = 0.04 = 4\%

The bank pays 4 percent a year.

2Apply it to Sua's deposit

#7 Identify Subproblems 7.RP.A.3

The same rate on 600,000 won.

600{,}000 \times 0.04 = 24{,}000

She earns 24,000 won of interest.

3Add the deposit back

#13 Convert to Algebra 7.RP.A.3

Withdrawing in all means her own money plus what it earned.

600{,}000 + 24{,}000 = 624{,}000

624,000 won in total.

Answer: 624,000 won

4 · Reviewdoes it hold up?

Her interest divided by her deposit is 0.04 again, the same rate the first deposit showed -- which is what a fixed rate means.

Another way: Scaling the first deposit's interest in the ratio $600{,}000 : 700{,}000$ skips the percentage and lands on the same 24,000 won; the rate is worth finding anyway because it is what the bank advertises.

Standardsmin grade 7

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems — Working out simple interest at a given rate.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Reading the first deposit as a rate rather than a comparison.

💡Takeaway. Interest is a share of what you put in. When you take it out, you get your own money back too.

Interest is a rate on the principal, and the principal comes back too · 12 practice problems

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