Tyler buys a stereo system for $1200, and pays for it using a credit card. This particular card charges 1.5 percent monthly interest on the unpaid balance, and requires a minimum payment of $20 each month. Suppose that Tyler pays only the minimum amount each month. How long will it take Tyler to pay off the debt in this way, and how much will the bank eventually receive for its $1200 loan to Tyler?

Question

Tyler buys a stereo system for $1200, and pays for it using a credit card. This particular card charges 1.5 percent monthly interest on the unpaid balance, and requires a minimum payment of $20 each month. Suppose that Tyler pays only the minimum amount each month. How long will it take Tyler to pay off the debt in this way, and how much will the bank eventually receive for its $1200 loan to Tyler?

Answer 1

To calculate how long it will take Tyler to pay off the debt and how much the bank will eventually receive, we need to consider the monthly interest and the minimum payment.

First, let's calculate the interest charged each month. The credit card charges 1.5 percent monthly interest on the unpaid balance. Since the balance is $1200, the monthly interest amount is:

Interest = (1.5/100) * $1200 = $18

Now, let's consider the minimum payment. Tyler is required to make a minimum payment of $20 each month. This means he will pay $20 towards the debt every month.

To figure out how long it will take Tyler to pay off the debt, we need to calculate the number of months it will take for the unpaid balance to reach $0. Each month, the unpaid balance decreases by the minimum payment minus the interest charged.

Let's calculate the number of months:

Unpaid Balance = $1200
Minimum Payment = $20
Monthly Interest = $18

Month 1: $1200 - $20 + $18 = $1198
Month 2: $1198 - $20 + $18 = $1196
Month 3: $1196 - $20 + $18 = $1194
...
Month n: $20 - $18 = $2 (Here, the unpaid balance would become $2, and it will take one more month to fully pay off the remaining amount.)

Since Tyler pays only the minimum each month, it takes a total of n + 1 months to pay off the debt completely.

Now, let's calculate how much the bank will eventually receive from Tyler's $1200 loan:

Bank's total interest = (n + 1) * $18
Bank's total payment = $1200 + Bank's total interest

Substituting the values, we get:

Bank's total interest = (n + 1) * $18
Bank's total payment = $1200 + (n + 1) * $18

And that's how we can calculate how long it will take Tyler to pay off the debt and how much the bank will eventually receive.