Answer: D) $819
Step-by-step explanation:
To calculate the interest paid by Blake in month 2, we need to first calculate the monthly payment using the loan amount and interest rate. We can use the formula for the present value of an annuity to find the monthly payment.
Present value of annuity formula:
PMT = PV * (r / (1 - (1 + r)^-n))
Where:
PV = present value (loan amount) = $10,000
r = interest rate per period (monthly) = 4.5% / 12 = 0.375%
n = total number of periods (months) = 12
PMT = $876.07 (rounded to the nearest cent)
Next, we can use the formula for the future value of an annuity to find the balance of the loan after the first month.
Future value of annuity formula:
FV = PMT * ((1 + r)^n - 1) / r
Where:
PMT = monthly payment = $876.07
r = interest rate per period (monthly) = 0.375%
n = number of periods (months) = 1
FV = $8,917.16
Therefore, the interest paid in month 2 can be calculated by finding the difference between the balance of the loan after the first month and the balance of the loan after the second month. The interest paid is the difference between these two values.
Balance after first month = $8,917.16
Balance after second month = $8,834.53
Interest paid in month 2 = $82.63 (rounded to the nearest cent)
Therefore, the closest answer choice is option D) $819.