Robert Mason's account of $98.50 has been delinquent for three months. According to the office procedures manual, after 90 days a 2% service charge, compounded monthly, is added to future bills. What will be the amount owed after nine months?
Pt = Po
Pt = Po
Pt = Po (r + 1)^n.
r =2% / 100% = 0.02 = rate / mo.
n = 12 comp/yr * 0.75 yr = 9 comp.
Pt = 98.50 (1.02 )^9,
Pt = 98.50 * 1.1951 =117.72 after 9mo.
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To calculate the amount owed after nine months, we need to determine the service charge for each month and add it to the initial balance.
First, let's calculate the service charge for each month:
2% of $98.50 = $1.97 (rounded to two decimal places)
Since the service charge is compounded monthly, we need to calculate the service charge for each month separately and add it to the balance.
After the first month, the balance will be:
$98.50 + $1.97 = $100.47
After the second month, the balance will be:
$100.47 + $1.97 = $102.44
After the third month, the balance will be:
$102.44 + $1.97 = $104.41
From the fourth to the ninth month, we'll continue adding $1.97 each month:
After the fourth month:
$104.41 + $1.97 = $106.38
After the fifth month:
$106.38 + $1.97 = $108.35
After the sixth month:
$108.35 + $1.97 = $110.32
After the seventh month:
$110.32 + $1.97 = $112.29
After the eighth month:
$112.29 + $1.97 = $114.26
After the ninth month:
$114.26 + $1.97 = $116.23
Therefore, the amount owed after nine months will be $116.23.
To calculate the amount owed after nine months, we need to consider the delinquent amount of $98.50 and the 2% service charge compounded monthly.
First, let's calculate the service charge for each month. The service charge is 2% of the delinquent amount, which is $98.50.
Monthly service charge = 2% of $98.50
= (2/100) * $98.50
= $1.97 (rounded to two decimal places)
Now, the service charge for the second month will be based on the sum of the delinquent amount and the service charge from the first month, which is $98.50 + $1.97 = $100.47.
We repeat this process for each subsequent month. Here's a breakdown of the delinquent amount and service charges over a period of nine months:
Month 1: Delinquent amount = $98.50 | Service charge = $1.97
Month 2: Delinquent amount = $100.47 | Service charge = $2.01
Month 3: Delinquent amount = $102.48 | Service charge = $2.05
Month 4: Delinquent amount = $104.53 | Service charge = $2.09
Month 5: Delinquent amount = $106.62 | Service charge = $2.13
Month 6: Delinquent amount = $108.75 | Service charge = $2.17
Month 7: Delinquent amount = $110.92 | Service charge = $2.22
Month 8: Delinquent amount = $113.14 | Service charge = $2.26
Month 9: Delinquent amount = $115.40 | Service charge = $2.31
Now, to find the amount owed after nine months, we need to add up the delinquent amount and all the service charges:
Amount owed after nine months = Delinquent amount + Sum of service charges
= $98.50 + ($1.97 + $2.01 + $2.05 + $2.09 + $2.13 + $2.17 + $2.22 + $2.26 + $2.31)
= $98.50 + $19.21
= $117.71 (rounded to two decimal places)
Therefore, the amount owed after nine months will be $117.71.