Reasoning Tommy earned ​$14.80 in interest after 4 years on a principal of ​$100. His simple interest rate is 3.7​%. Jane earned ​$61.50 in interest after 3 years on a principal of ​$500. Her simple interest rate is 4.1​%. Which bank would you rather​ use, Tommy's or​ Jane's? Explain your reasoning.

Question

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Part 1
Which bank would you rather​ use?
A.
Tommy's because his bank paid more interest.
B.
Jane's because her bank offers a better interest rate.
C.
Tommy's because his investment took less time.
D.
Jane's because her bank acc

Answer 1

To determine which bank to choose, we can examine both the interest rates and the total amount earned in interest over the specified periods.

Tommy's Bank:

• Principal: $100
• Interest earned: $14.80
• Time: 4 years
• Interest Rate: 3.7%

We can confirm the interest rate calculation using the simple interest formula: \[ I = P \times r \times t \] Where \( I \) is interest, \( P \) is principal, \( r \) is the rate (in decimal), and \( t \) is time in years.

In Tommy's case: \[ 14.80 = 100 \times r \times 4 \] \[ r = \frac{14.80}{400} = 0.037 \text{ or } 3.7% \]

Jane's Bank:

• Principal: $500
• Interest earned: $61.50
• Time: 3 years
• Interest Rate: 4.1%

Using the same simple interest formula for Jane: \[ 61.50 = 500 \times r \times 3 \] \[ r = \frac{61.50}{1500} = 0.041 \text{ or } 4.1% \]

Comparison:

• Interest Rate: Jane's bank has a higher interest rate (4.1%) compared to Tommy's bank (3.7%).
• Interest Earned Relative to Principal and Time: Jane earns more interest ($61.50) in a shorter time (3 years) despite her principal being higher.

Conclusion:

Considering both the interest rate and the total interest earned, the best choice would be: B. Jane's because her bank offers a better interest rate.

This indicates that Jane's bank provides a higher return on investment per dollar and earns more interest in the given time frame.