You and your friend go to the store to buy a new set of headphones when they release. The headphones cost $150. You use your debit card to buy the headphones. Your friend uses their credit card to buy the headphones. Their credit card has a monthly interest rate of 2%. If it takes your friend a year to pay off the headphones, who spends less on the purchase and by how much?(1 point)

Question

Responses

Your friend spends $36 less than you.
Your friend spends $36 less than you.

You spend $3 less than your friend.
You spend $3 less than your friend.

Your friend spends $3 less than you.
Your friend spends $3 less than you.

You spend $36 less than your friend.

Answer 1

Let's break down the costs for both you and your friend.

1. Your purchase (debit card):

   • You pay $150 upfront with your debit card.
   • Therefore, your total cost is $150.

2. Your friend's purchase (credit card):

   • Your friend buys the headphones on a credit card for $150.
   • The monthly interest rate is 2%, which means the annual interest rate is \(2% \times 12 = 24%\).

To calculate your friend's total payment at the end of the year, we can use the formula for simple interest:

\[ \text{Total payment} = \text{Principal} \times (1 + \text{interest rate}) \]

Where:

• Principal = $150
• Interest rate for one year = 24% = 0.24

Now, calculating:

\[ \text{Total payment} = 150 \times (1 + 0.24) = 150 \times 1.24 = 186 \]

So your friend will end up paying $186 after one year.

3. Comparing costs:

• Your total cost = $150
• Your friend's total cost = $186

Now we can find out who spends less and by how much:

\[ 186 - 150 = 36 \]

Therefore, your friend spends $36 more than you.

Conclusion: You spend $36 less than your friend.