Question

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:

Step1: Recall the simple interest formula

The formula for simple interest is \( I = P \cdot r \cdot t \), where \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal form), and \( t \) is the time in years. Here, \( P=\$45,000 \).

Step2: Calculate interest for Option 1

For Option 1: \( r = 2\%=0.02 \), \( t = 5 \) years.
\( I_1=45000\times0.02\times5 \)
\( I_1 = 45000\times0.1=4500 \) dollars.

Step3: Calculate interest for Option 2

For Option 2: \( r = 3\% = 0.03 \), \( t = 3 \) years.
\( I_2=45000\times0.03\times3 \)
\( I_2=45000\times0.09 = 4050 \) dollars.

Step4: Calculate interest for Option 3

For Option 3: \( r = 1\%=0.01 \), \( t = 7 \) years.
\( I_3=45000\times0.01\times7 \)
\( I_3=45000\times0.07 = 3150 \) dollars.

Step5: Compare the interests

Compare \( I_1 = 4500 \), \( I_2 = 4050 \), and \( I_3 = 3150 \). We see that \( 3150<4050<4500 \).

Answer:

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