Monica deposits ​$200 into a savings account that pays a simple interest rate of 4.2​%. Paul deposits ​$300 into a savings account that pays a simple interest rate of 3.5​%. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she​ correct? Justify your response.

Question

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Part 1
▼
Monica is incorrect.
Monica is correct.
Monica will earn ​$
  
enter your response here in 1 year while Paul will earn ​$
  
enter your response here in 1 year.

Answer 1

To determine if Monica or Paul will earn more interest in 1 year, we can use the formula for simple interest:

\[ I = P \times r \times t \]

where:

• \( I \) = interest earned
• \( P \) = principal amount (initial deposit)
• \( r \) = interest rate (as a decimal)
• \( t \) = time (in years)

Calculating Monica's Interest

Monica's deposit:

• Principal (\( P \)) = $200
• Interest rate (\( r \)) = 4.2% = 0.042
• Time (\( t \)) = 1 year

\[ I_M = 200 \times 0.042 \times 1 = 200 \times 0.042 = 8.40 \]

Calculating Paul's Interest

Paul's deposit:

• Principal (\( P \)) = $300
• Interest rate (\( r \)) = 3.5% = 0.035
• Time (\( t \)) = 1 year

\[ I_P = 300 \times 0.035 \times 1 = 300 \times 0.035 = 10.50 \]

Summary of Interest Earned

• Monica will earn \( I_M = 8.40 \) in 1 year.
• Paul will earn \( I_P = 10.50 \) in 1 year.

Conclusion

Monica will not earn more interest than Paul despite her higher interest rate because her principal amount is smaller. Thus, Monica is incorrect.

Monica will earn $8.40 in 1 year while Paul will earn $10.50 in 1 year.