To determine which bank would charge Michelle the least amount of interest, we will calculate the total interest for both banks using the formula for simple interest:
\[ \text{Interest} = P \times r \times t \]
where:
- \(P\) is the principal amount (the amount borrowed).
- \(r\) is the annual interest rate (as a decimal).
- \(t\) is the time the money is borrowed for (in years).
Bank A:
- Principal \(P = 4500\)
- Annual interest rate \(r = 9% = 0.09\)
- Time \(t = 6\) years
Calculating the interest for Bank A:
\[ \text{Interest} = 4500 \times 0.09 \times 6 \]
\[ \text{Interest} = 4500 \times 0.54 = 2430 \]
Bank B:
- Principal \(P = 4500\)
- Annual interest rate \(r = 11% = 0.11\)
- Time \(t = 4\) years
Calculating the interest for Bank B:
\[ \text{Interest} = 4500 \times 0.11 \times 4 \]
\[ \text{Interest} = 4500 \times 0.44 = 1980 \]
Summary of Interest:
- Interest charged by Bank A: $2430
- Interest charged by Bank B: $1980
Conclusion: Bank B would charge Michelle the least amount of interest, totaling $1980, compared to Bank A's total of $2430.
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