Question

1. scott wants to take out a $45,000 loan to buy a new car. which of the following options would allow him to pay the least amount of interest? select one correct answer. option 1: a 5 - year loan with a 2% simple interest rate option 2: a 3 - year loan with a 3% simple interest rate option 3: a 7 - year loan with a 1% simple interest rate

Explanation:

To determine which option has the least interest, we use the simple interest formula \( I = P \times r \times t \), where \( P = 45000 \), \( r \) is the annual interest rate (in decimal), and \( t \) is the time in years.

Step 1: Calculate interest for Option 1

\( r = 2\% = 0.02 \), \( t = 5 \)
\( I_1 = 45000 \times 0.02 \times 5 \)
\( I_1 = 45000 \times 0.1 = 4500 \)

Step 2: Calculate interest for Option 2

\( r = 3\% = 0.03 \), \( t = 3 \)
\( I_2 = 45000 \times 0.03 \times 3 \)
\( I_2 = 45000 \times 0.09 = 4050 \)

Step 3: Calculate interest for Option 3

\( r = 1\% = 0.01 \), \( t = 7 \)
\( I_3 = 45000 \times 0.01 \times 7 \)
\( I_3 = 45000 \times 0.07 = 3150 \)

Now we compare \( I_1 = 4500 \), \( I_2 = 4050 \), and \( I_3 = 3150 \). The smallest interest is \( 3150 \) from Option 3.

Answer:

Option 3: A 7-year loan with a 1% simple interest rate