Final answer:
To calculate the monthly payment, or x, for a $34,000 loan with a nominal monthly interest rate of 9.4%, an annuity formula is used that requires the loan amount, interest rate per month, and number of monthly payments. The nominal annual interest rate is converted to a monthly rate for the calculation.
Step-by-step explanation:
To determine what the monthly payment, or x, should be for a loan of $34,000 with a nominal monthly interest rate of 9.4%, we can use the formula for an ordinary annuity. Since payments are made at the end of each month, this situation is modeled as an annuity. The formula incorporates the total loan amount (PV), the nominal interest rate per period (i), and the total number of payments (n).
The formula for the monthly payment on an annuity is PV = R * [(1 - (1 + i)^-n) / i], where PV is the present value of the loan, R is the periodic (monthly) payment, i is the monthly interest rate, and n is the number of payments.
The nominal interest rate needs to be converted to a monthly rate by dividing by 12. Thus, for a rate of 9.4% annually, the monthly rate is 0.094/12. To solve for R, the formula needs to be rearranged, which typically requires a financial calculator or software capable of handling such calculations. It is important to note that the actual payment could differ slightly based on rounding and the method used by the lender for calculation.