Question

kanya has a credit card that gives a 6% discount on every purchase and free shipping when used online. the annual percentage rate on the credit card is 12%. kanya wants to buy a laptop that costs $420. which statement about the cost of the laptop is true?

• if kanya uses the credit card and pays the full balance during the billing cycle, she will spend $25.20 more than paying cash for the laptop.
• if kanya uses the credit card and pays the full balance during the billing cycle, she will spend $50.40 more than paying cash for the laptop.
• if kanya uses the credit card and pays the full balance during the billing cycle, she will spend $50.40 less than paying cash for the laptop.
• if kanya uses the credit card and pays the full balance during the billing cycle, she will spend $25.20 less than paying cash for the laptop.

Explanation:

Step1: Calculate discount amount

The discount rate is 6% and the cost of the laptop is $420. To find the discount, we calculate 6% of 420. The formula for percentage discount is $\text{Discount} = \text{Rate} \times \text{Original Price}$. So, $6\%$ of $420$ is $0.06 \times 420$.
$0.06\times420 = 25.20$

Step2: Analyze cost when paying full balance

When Kanya pays the full balance during the billing cycle, she doesn't have to pay the annual percentage rate (interest) because she is paying off the balance. So, she only pays the discounted price. The discounted price is the original price minus the discount, which is $420 - 25.20 = 394.80$. If she pays cash, she pays $420$. The difference between paying cash and using the credit card (and paying full balance) is $420 - 394.80 = 25.20$. So, she spends $25.20$ less when using the credit card and paying full balance.

Answer:

If Kanya uses the credit card and pays the full balance during the billing cycle, she will spend $25.20 less than paying cash for the laptop. (The option corresponding to this statement)