Answer:
Explanation:
To calculate Bill's monthly payment, we can use the formula for the monthly payment on a loan:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
- P = Monthly payment
- r = Monthly interest rate
- PV = Present value or outstanding balance
- n = Number of months
In this case, the outstanding balance is $3200, and the loan term is 18 months. The monthly interest rate can be calculated by dividing the annual interest rate by 12. The annual interest rate is 9.3%.
r = 9.3% / 12 = 0.775% (expressed as a decimal)
Now we can substitute the values into the formula:
P = (0.00775 * 3200) / (1 - (1 + 0.00775)^(-18))
Using a calculator, we can solve for P:
P ≈ $191.47
Therefore, Bill's monthly payment will be approximately $191.47.
To calculate the effective rate of interest the bank is charging Bill, we can use the formula:
Effective Rate = (1 + r/n)^n - 1
Where:
- r = Annual interest rate
- n = Number of compounding periods per year
In this case, the annual interest rate is 9.3% and the compounding is monthly, so n = 12.
Substituting the values into the formula:
Effective Rate = (1 + 0.093/12)^12 - 1
Using a calculator, we can solve for the effective rate:
Effective Rate ≈ 9.55%
Therefore, the bank is charging Bill an effective rate of interest of approximately 9.55%.