i need help writing this out..
You have a credit card with a balance of $754.43 at a 13.6% APR. You have $300.00 available each month to save or pay down your debts.
a. How many months will it take to pay off the credit card if you only put half of the available money toward the credit card each month and make the payments at the beginning of the month?
b. How many months will it take to pay off the credit card if you put all of the available money toward the credit card each month and make the payments at the beginning of the month?
a. It will take approximately 24 months to pay off the credit card if you only put half of the available money toward the credit card each month and make the payments at the beginning of the month.
b. It will take approximately 12 months to pay off the credit card if you put all of the available money toward the credit card each month and make the payments at the beginning of the month.
a. Well, let's do some clown math, shall we? If you only put half of the available money toward the credit card each month, that would be $150.00. So, the remaining half can be used for something fun, like buying a clown wig! Anyway, let's calculate how many months it will take to pay off the credit card.
First, let's figure out the monthly interest rate. The APR is 13.6%, so divide that by 12 (since there are 12 months in a year) to get 1.13%. We'll need to convert that to a decimal, so it becomes 0.0136.
Now, in the first month, you'll pay $150 towards the credit card. Since you make the payments at the beginning of the month, you won't accrue any interest on that payment. The remaining balance would be $754.43 - $150 = $604.43.
Next month, you'll have to pay interest on the remaining balance of $604.43. Multiply that by the monthly interest rate (0.0136) to get the interest charged for that month. Subtract that from the $150 you're paying, and the remaining balance would be $604.43 + interest - $150.
Repeat this process each month, adjusting the remaining balance with the added interest and subtracting the $150 payment. Keep doing this until the remaining balance reaches zero. Count how many months it takes, and you'll have your answer!
b. Now, if you put all $300 towards the credit card each month, you'll have a clownishly speedy debt payoff. Since you're making the payments at the beginning of the month, you won't accrue any interest on the payments. So, each month, you'll subtract $300 from the outstanding balance ($754.43) until it reaches zero.
Divide the outstanding balance by $300 and that gives you the number of full months it will take to pay off the credit card. Remember to round up because clowns always like to err on the side of caution!
I hope that helps, and remember, don't clown around too much with credit cards!
To write out the solution, we'll follow these steps:
Step 1: Calculate the monthly interest rate
Step 2: Determine the monthly payment for each scenario
Step 3: Calculate the number of months to pay off the credit card for each scenario
Let's tackle each part one by one.
a. How many months will it take to pay off the credit card if you only put half of the available money toward the credit card each month and make the payments at the beginning of the month?
Step 1: Calculate the monthly interest rate
The annual percentage rate (APR) is given as 13.6%. To calculate the monthly interest rate, divide it by 12 (months). We'll get 1.13.6/12 = 1.13%.
Step 2: Determine the monthly payment for this scenario
You have $300.00 available each month, but you'll only put half of that amount toward the credit card, so it'll be $150.00.
Step 3: Calculate the number of months to pay off the credit card
We'll use an iterative process to find the number of months needed to pay off the credit card.
- Start with the initial balance: $754.43.
- Subtract the monthly payment of $150.00.
- Add the monthly interest on the remaining balance (balance multiplied by monthly interest rate).
- Repeat the above steps until the balance becomes zero.
Let's calculate it step by step until the balance reaches zero:
Month 1:
Balance = $754.43 - $150.00 = $604.43
Interest = $604.43 * (1.13/100) = $6.84
Month 2:
Balance = $604.43 - $150.00 + $6.84 = $461.27
Interest = $461.27 * (1.13/100) = $5.21
Continue this process until the balance becomes zero. Count the number of months it takes to reach zero.
b. How many months will it take to pay off the credit card if you put all of the available money toward the credit card each month and make the payments at the beginning of the month?
Step 1: Calculate the monthly interest rate (same as in part a, 1.13%)
Step 2: Determine the monthly payment for this scenario (full $300.00)
Step 3: Calculate the number of months using the iterative process described in part a, but with a monthly payment of $300.00 instead of $150.00.
Continue the iterations until the balance reaches zero and count the number of months it takes.
Note: Since the calculations involve a step-by-step process and can be quite lengthy, it's recommended to use a spreadsheet or a calculator to simplify the calculations and obtain the final answers.
To find the answers to these questions, we need to use some mathematical calculations. Here's how you can work through it step by step:
a. How many months will it take to pay off the credit card if you only put half of the available money toward the credit card each month and make the payments at the beginning of the month?
1. First, find out how much money you will be putting towards the credit card each month. Since you have $300.00 available each month, half of that amount will be $150.00.
2. Next, calculate the interest charged on the remaining balance at the beginning of each month. To do this, multiply the balance by the APR (13.6% or 0.136), then divide by 12 (months in a year) to find the monthly interest rate. For instance, ($754.43 * 0.136) / 12 = $8.50.
3. Subtract the amount you are paying towards the credit card (half of the available money) from the interest charged. In this case, $8.50 - $150.00 = -$141.50.
4. With a negative result, it means you have overpaid on the card. If we assume that the negative result carries over to the next month and further payments are made in the same way (paying half of the available money), this means the card will be completely paid off in the first month.
Therefore, it will take only 1 month to pay off the credit card if you put half of the available money toward it each month.
b. How many months will it take to pay off the credit card if you put all of the available money toward the credit card each month and make the payments at the beginning of the month?
1. Since you are putting all of the available money ($300.00) towards the credit card each month, there will be no additional interest charges applied.
2. Divide the starting balance of $754.43 by the monthly payment of $300.00. Round up the result to the nearest whole number to determine how many months it will take to pay off the credit card. In this case, $754.43 / $300.00 = 2.51. Rounded up, it will take 3 months to pay off the credit card.
Therefore, it will take 3 months to pay off the credit card if you put all of the available money toward it each month.