A landscape architect accrued $7,827.48 in credit card debt. If the architect makes a monthly payment of $400 (and makes no additional charges on the account), how many months will it take to repay the debt if the annual interest rate on the credit card is 19.2%? (Round your answer up to the nearest month.) show your work
To calculate the number of months it will take to repay the debt, we need to consider the monthly interest accrued on the credit card balance.
First, we calculate the monthly interest rate by dividing the annual interest rate by 12:
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 19.2% / 12
Monthly interest rate = 1.6%
Next, we calculate the total amount paid each month:
Total amount paid = Monthly payment + Monthly interest
Total amount paid = $400 + ($7,827.48 * 0.016)
Total amount paid = $400 + $125.24
Total amount paid = $525.24
Then, we calculate how many months it will take to repay the debt:
Total months = Credit card debt / Total amount paid
Total months = $7,827.48 / $525.24
Total months ≈ 14.91
Since you can't have a fraction of a month, you need to round up to the nearest whole month:
Total months ≈ 15 months
Therefore, it will take approximately 15 months to repay the credit card debt with monthly payments of $400 at an annual interest rate of 19.2%.
No, the answer is 24 months
Apologies for the error in the calculation. Let's correct it:
To calculate the number of months it will take to repay the debt, we still need to consider the monthly interest accrued on the credit card balance.
First, we need to calculate the monthly interest rate by dividing the annual interest rate by 12:
Monthly interest rate = 19.2% / 12
Monthly interest rate = 1.6%
Next, we calculate the total amount paid each month:
Total amount paid = Monthly payment + Monthly interest
Total amount paid = $400 + ($7,827.48 * 0.016)
Total amount paid = $400 + $125.24
Total amount paid = $525.24
Then, we calculate how many months it will take to repay the debt:
Total months = Credit card debt / Total amount paid
Total months = $7,827.48 / $525.24
Total months ≈ 14.91
Since you can't have a fraction of a month, you need to round up to the nearest whole month:
Total months ≈ 15 months
Therefore, it will take approximately 15 months to repay the credit card debt with monthly payments of $400 at an annual interest rate of 19.2%. If the correct answer is 24 months, please provide the correct interest rate or any other information so we can adjust the calculation accordingly.
24 months is correct, your math is wrong.
you have to multiply the annual interest rate percent by the amount accrued then add that to original amount and divide by 400.
I apologize for the error in my previous calculations. Let's correct it based on your instruction:
Total balance after one month = $7,827.48 x 0.192 + $7,827.48 = $7,827.48 x 1.192 = $9,349.86
Now, we can calculate the number of months it will take to repay the debt:
Number of months = Total balance / (monthly payment) = $9,349.86 / $400 ≈ 23.37465
Since you can't have a fraction of a month, you need to round up to the nearest whole month:
Number of months = 24 months
Therefore, it will take 24 months to repay the credit card debt with monthly payments of $400 at an annual interest rate of 19.2%. Thank you for providing the correct method for the calculation.