Picabo borrows $1,000. To repay the amount she makes 12 equal monthly payments of $90.30. Determine the following:
(a) The effective monthly interest rate
(b) The nominal annual interest rate
(c) The effective annual interest rate
To determine the effective monthly interest rate, we need to calculate the interest paid per month by subtracting the principal amount from the total repayment amount and then dividing it by the number of months.
(a) The effective monthly interest rate can be calculated using the following formula:
Effective Monthly Interest Rate = (Total Payments - Principal) / (Number of Months)
In this case, the total payments are calculated by multiplying the monthly payment amount by the number of months. So, the total repayment is 12 * $90.30 = $1,083.60.
Therefore, the effective monthly interest rate is ($1,083.60 - $1,000) / 12 = $83.60 / 12 = $6.9667.
(b) The nominal annual interest rate can be determined by multiplying the effective monthly interest rate by the number of months in a year, namely 12.
Nominal Annual Interest Rate = Effective Monthly Interest Rate * 12
In this case, the nominal annual interest rate is $6.9667 * 12 = 83.6%.
(c) The effective annual interest rate can be calculated using the following formula:
Effective Annual Interest Rate = (1 + Effective Monthly Interest Rate) ^ 12 - 1
In this case, the effective monthly interest rate is 0.069667 (6.9667%).
Therefore, the effective annual interest rate is (1 + 0.069667) ^ 12 - 1 = 1.9402274 - 1 = 0.9402274 or 94.02%.