3. a customer applied for a loan for $15,000 to buy a motorcycle. the customer qualified for different loan…

3. a customer applied for a loan for $15,000 to buy a motorcycle. the customer qualified for different loan options. which loan option would allow the customer to pay the least amount of interest?\na. a 3 - year loan with an 7% annual simple interest rate\nb. a 4 - year loan with a 5% annual simple interest rate\nc. a 5 - year loan with a 4.5% annual simple interest rate\nd. a 6 - year loan with a 3.7% annual simple interest rate

Answer

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Here, $P=$15000$.

Step2: Calculate interest for option a

For option a, $t = 3$ years and $r=0.07$. Then $I_a=Prt=15000\times0.07\times3 = 15000\times0.21=$3150$.

Step3: Calculate interest for option b

For option b, $t = 4$ years and $r = 0.05$. Then $I_b=Prt=15000\times0.05\times4=15000\times0.2=$3000$.

Step4: Calculate interest for option c

For option c, $t = 5$ years and $r = 0.045$. Then $I_c=Prt=15000\times0.045\times5=15000\times0.225=$3375$.

Step5: Calculate interest for option d

For option d, $t = 6$ years and $r = 0.037$. Then $I_d=Prt=15000\times0.037\times6=15000\times0.222=$3330$.

Answer:

B. A 4 - year loan with a 5% annual simple interest rate