Final answer:
To calculate Bryan's monthly car payment, we convert the 8.4% annual interest rate to a monthly rate and use the loan payment formula, considering the principal amount of $244,000 and the 5-year loan term. Bryan will then make fixed monthly payments based on this calculation.
Step-by-step explanation:
To answer the question of the monthly payment Bryan must make for his new car priced at $244,000 with an interest rate of 8.4% compounded semi-annually over 5 years, we use the formula for calculating the payment (PMT) on an installment loan. The formula takes into account the principal amount (P), the number of payment periods (n), and the periodic interest rate (i).
First, we convert the annual interest rate to the monthly rate. Since the interest is compounded semi-annually, we divide it by 2 to get the semi-annual rate, and then divide by 6 to get the monthly rate. For an 8.4% annual rate, the monthly interest rate (i) is 0.84%/2/6 = 0.007.
Next, we calculate the number of payment periods by multiplying the number of years by 12 (since payments are monthly). For 5 years, this results in 5 * 12 = 60 payment periods.
The formula for the monthly payment is given by:
PMT = P * (i/(1 - (1 + i)^(-n)))
By substituting the given values:
PMT = 244,000 * (0.007 / (1 - (1 + 0.007)^(-60)))
This results in a monthly payment amount that Bryan will need to make to repay the loan. Calculations must be done using a financial calculator or appropriate software to obtain the precise monthly payment amount.