Robert's acct p $98.50 has been delinquent for three months. Office procedures charge a 2% service charge after 90 days componded monthly and is added to future bills. What will be the amount owed after nine months? I did $98.50 x 2% = $1.97 $1.97 x 6months = $11.82 $98.50+ $11.82 = $110.32. Check my math. Please give breakdown out of school 40 yrs Thanks
To calculate the amount owed after nine months, we need to consider the compounded monthly service charges added to the original balance.
First, let's calculate the service charge for each month. The service charge is calculated as 2% of the delinquent amount:
2% of $98.50 = $1.97 (rounding to two decimal places)
To find the amount owed after each month, we will add the service charge to the previous amount owed:
Month 1: $98.50 + $1.97 = $100.47
Month 2: $100.47 + $1.97 = $102.44
Month 3: $102.44 + $1.97 = $104.41
After the third month, the service charges start compounding. Let's calculate the amount owed for the next six months:
Month 4: $104.41 + $1.97 = $106.38
Month 5: $106.38 + $1.97 = $108.35
Month 6: $108.35 + $1.97 = $110.32
Month 7: $110.32 + $1.97 = $112.29
Month 8: $112.29 + $1.97 = $114.26
Month 9: $114.26 + $1.97 = $116.23
Therefore, the amount owed after nine months would be $116.23, not $110.32 as you calculated initially.
To calculate the amount owed after nine months, you need to consider the delinquency period of three months and the 2% service charge applied after 90 days.
First, let's calculate the service charge for three months.
1. Calculate the daily interest rate by dividing 2% by 30 days: 2% / 30 = 0.0667% (approximately)
2. Multiply the daily interest rate by the number of delinquent days (3 months x 30 days): 0.0667% x 90 = 6%
So, the service charge for the three-month period is 6% of $98.50, which is $5.91.
Next, let's calculate the service charge that will be compounded monthly and added to future bills for the next six months.
1. Divide the annual interest rate (2%) by 12 to get the monthly interest rate: 2% / 12 = 0.1667% (approximately)
2. Calculate the future value of the service charge using the formula for compound interest:
Future value = Present value × (1 + Monthly interest rate)^Number of compounding periods
Future value = $5.91 × (1 + 0.1667%)^6 = $5.91 × (1 + 0.001667)^6
Note: Since the service charge is compounded monthly, we raise the factor (1 + Monthly interest rate) to the power of the number of compounding periods (6 months).
Now, let's calculate the future value of the service charge:
Future value ≈ $5.91 × (1.001667)^6 ≈ $5.91 × 1.010004 ≈ $5.96
Therefore, the total service charge after nine months is approximately $5.91 (for the first three months) + $5.96 (for the next six months) = $11.87 (rounded to two decimal places).
Finally, add the service charge to the initial amount owed:
Total amount owed = $98.50 + $11.87 = $110.37 (rounded to two decimal places).
So, the correct calculation would be $98.50 + $11.87 = $110.37, not $110.32 as you originally calculated.
I hope this breakdown helps! Let me know if you have further questions.