John's account of 98.50 has been delinquent for 3 months. After 90 days office charges a 2% service charge, compounded monthly that is added to future bills. What would be the amount owed after 9 months? My math is 98.50 x 0.02 = 1.97 1.97 x 12 months = 23.64. Take 3 months off that and it leaves 17.73 add that to 98.50 = 116.23 for nine months. Please give break down Thanks
You did simple interest, supposed to compound and where did 12 months come from? It says 9 months.
compound for 6 months (9 months - 3 months)
98.50 * (1.02)^6
=98.50*1.12616
=110.93
How did you come up with (1.02)
To calculate the amount owed after 9 months, we need to consider the initial balance, the service charge, and the compounding effect.
1. Calculate the service charge after 3 months:
- Multiply the initial balance of $98.50 by the service charge rate of 2%: 98.50 x 0.02 = $1.97.
- This represents the amount charged after 3 months.
2. Calculate the compounding effect of the service charge over the next 6 months:
- Since the office charges the service fee monthly, we need to calculate the compounding effect over the remaining 9 months (total of 9 - 3 = 6 months).
- The compounding formula is A = P(1 + r/n)^(nt), where:
- A = the future value (amount owed after 9 months)
- P = the principal amount (initial balance + service charge after 3 months)
- r = the annual interest rate (2%, or 0.02)
- n = the number of compounding periods per year (monthly, so n = 12)
- t = time in years (6/12 = 0.5 years, since we have 6 months left)
- Plugging in the values, we get A = (98.50 + 1.97) * (1 + 0.02/12)^(12 * 0.5).
3. Calculate the total amount owed after 9 months:
- Add the initial balance (98.50) and the compounded service charge from step 2 together.
Therefore, the step-by-step breakdown of the calculation would be:
1. Service charge after 3 months: $1.97
2. Compounded service charge over 6 months: (98.50 + 1.97) * (1 + 0.02/12)^(12 * 0.5)
3. Total amount owed after 9 months: Initial balance (98.50) + Compounded service charge
Evaluate the expressions to find the final answer.