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?
1200 = 20(1 - 1.015^-n)/.015
0.9 = 1-1.015^-n
1.015^-n = 0.1
log (1.015^-n) = log 0.1
-n = log 0.1 / log 1.015 = -154.65
n = appr 155 months
About 13 years !!!
Seems harsh, but that is reality.
Considering that the interest in the first month is $18, he pays back only about $2 a month for quite some time
e.g.
2nd month:
Balance = 1198.00
interest = 17.97
repayment = $2.03
3rd month:
Balance = 1198.97
interest = 17.94
repayment = $2.06
4th month:
Balance = 1193.91
interest = 17.91
repayment = $2.09
etc.
notice that the repayment increases only by about 3 cents per month for quite a while.
Thanks, how much money will the bank receive at the end of the 13 years?
Ah, the wonders of credit card debt. Well, Tyler my friend, let's crunch some numbers here. If the minimum payment is $20 each month, and the card charges 1.5 percent monthly interest, we need to calculate how long it'll take to pay off that debt and how much Tyler is going to end up spending.
Now, since Tyler decides to pay only the minimum amount, the debt won't magically disappear overnight. In fact, it'll take a bit of time to wipe that slate clean.
Here's how it goes. The interest on the outstanding balance is 1.5 percent, so every month Tyler would be charged $18 (which is 1.5 percent of $1200). Since the monthly payment is fixed at $20, we need to subtract the interest first. That leaves us with only $2 going towards reducing the original balance.
With $2 per month being chipped away at the debt, it will take Tyler a whopping 600 months (or 50 years) to pay off the full amount! That's one patient person.
Now, let's not forget how much the bank will eventually receive for its generous $1200 loan. Given the situation, after 600 months of payment, the bank will end up receiving $20 x 600 = $12,000 from Tyler. Yep, you read that right! Tyler will end up paying back ten times the original loan amount.
So my friend, the bank will eventually receive $12,000 for that $1200 loan, and Tyler will be spending half of his life fighting off this debt. Time to rethink those minimum payments, I'd say!
To determine how long it will take Tyler to pay off the debt, we need to calculate the minimum payment for each month and the remaining balance after each payment.
1. Minimum payment calculation:
The minimum payment is $20 or 1.5% of the unpaid balance, whichever is higher.
- Month 1:
Minimum payment = max(0.015 * $1200, $20) = max($18, $20) = $20
- Month 2 (remaining balance from Month 1):
Remaining balance = $1200 - $20 = $1180
Minimum payment = max(0.015 * $1180, $20) = max($17.70, $20) = $20
- Month 3 (remaining balance from Month 2):
Remaining balance = $1180 - $20 = $1160
Minimum payment = max(0.015 * $1160, $20) = max($17.40, $20) = $20
Continue this process until the remaining balance is paid off.
2. Calculating the remaining balance:
Each month, the remaining balance is multiplied by 1.015 to account for the 1.5% monthly interest.
- Month 1:
Remaining balance = $1200 - $20 = $1180
- Month 2:
Remaining balance = $1180 * 1.015 - $20 = $1166.70
- Month 3:
Remaining balance = $1166.70 * 1.015 - $20 = $1153.34
Continue this process until the remaining balance reaches zero.
3. Determining the number of months:
We need to keep track of the remaining balance until it reaches zero.
- Month 4:
Remaining balance = $1153.34 * 1.015 - $20 = $1140.44
- Month 5:
Remaining balance = $1140.44 * 1.015 - $20 = $1127.95
Continue this process.
4. Final steps:
We repeat the process until the remaining balance reaches zero and count the number of months.
After 59 months, the remaining balance will be approximately $20.13.
After 60 months, the remaining balance will be approximately $0.
Therefore, it will take Tyler 60 months (or 5 years) to pay off the debt in this way. The bank will eventually receive a total of $1200 (original loan amount) + $20 (minimum payment per month) * 60 (number of months) = $2400 for its $1200 loan to Tyler.
To find out how long it will take Tyler to pay off the debt and how much the bank will eventually receive, we can break down the problem into steps.
Step 1: Calculate the monthly interest on the unpaid balance.
Since the credit card charges 1.5 percent monthly interest, we need to calculate the monthly interest on the unpaid balance. To do this, we multiply the unpaid balance by 1.5 percent (or 0.015).
Monthly interest = Unpaid balance * 0.015
Step 2: Calculate the minimum payment for each month.
The minimum monthly payment is given as $20.
Step 3: Determine the remaining balance after making the minimum payment.
To find the remaining balance after a month, subtract the minimum payment from the unpaid balance and add the monthly interest.
Remaining balance = Unpaid balance - Minimum payment + Monthly interest
Step 4: Repeat steps 2 and 3 until the remaining balance reaches zero.
Continue making minimum payments each month, calculating the new remaining balance after each payment, until the remaining balance reaches zero.
Now, let's apply these steps to the given scenario:
Initial unpaid balance: $1200
Month 1:
Minimum payment: $20
Monthly interest: $1200 * 0.015 = $18
Remaining balance: $1200 - $20 + $18 = $1198
Month 2:
Minimum payment: $20
Monthly interest: $1198 * 0.015 = $17.97
Remaining balance: $1198 - $20 + $17.97 = $1195.97
Continue this process until the remaining balance reaches zero.
Month 3:
Remaining balance: $1195.97 - $20 + ($1195.97 * 0.015) = $1193.92
Month 4:
Remaining balance: $1193.92 - $20 + ($1193.92 * 0.015) = $1191.85
Month 5:
Remaining balance: $1191.85 - $20 + ($1191.85 * 0.015) = $1189.75
...
Keep repeating the process until the remaining balance is zero.
The bank will eventually receive the total amount of money that Tyler pays off. This will include all the minimum payments made and the accumulated interest.