Question

Michelle wants to borrow $4,500. Bank A will lend Michelle the money at a simple annual interest rate of 9% for 6 years. Bank B will lend her the money at 11% for 4 years. Which bank would charge Michelle the least amount of interest? Explain.

Answer 1

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.