Select the correct answer.Taylor wants to purchase a car with an auto loan. He can get a 48-month loan from his bank that is compounded monthly at an annual interest rate of 7.9%. Suppose Taylor needs to obtain a loan for $19,076 to purchase the car. Use the formula for the sum of a finite geometric series to determine Taylor's approximate monthly payment. P=1−(1+0)−48B,(0)A). Taylor's approximate monthly payment for the loan will be $458.35. B). Taylor's approximate monthly payment for the loan will be$464.81.C). Taylor's approximate monthly payment for the loan will be $546.50.D). Taylor's approximate monthly payment for the loan will be $4132.
Q. Select the correct answer.Taylor wants to purchase a car with an auto loan. He can get a 48-month loan from his bank that is compounded monthly at an annual interest rate of 7.9%. Suppose Taylor needs to obtain a loan for $19,076 to purchase the car. Use the formula for the sum of a finite geometric series to determine Taylor's approximate monthly payment. P=1−(1+0)−48B,(0)A). Taylor's approximate monthly payment for the loan will be $458.35. B). Taylor's approximate monthly payment for the loan will be$464.81.C). Taylor's approximate monthly payment for the loan will be $546.50.D). Taylor's approximate monthly payment for the loan will be $4132.
Calculate Monthly Interest Rate: Calculate the monthly interest rate from the annual rate.Annual interest rate = 7.9%Monthly interest rate = 127.9%= 0.6583%
Convert to Decimal Form: Convert the monthly interest rate into decimal form for calculation.Monthly interest rate (decimal) = 1000.6583= 0.006583
Use Amortizing Loan Formula: Use the formula for the monthly payment of an amortizing loan, which is different from the sum of a finite geometric series.Formula: P=1−(1+i)−nB⋅iWhere P is the monthly payment, B is the loan amount, i is the monthly interest rate, and n is the number of payments.B=$19,076, i=0.006583, n=48
Calculate Monthly Payment: Plug the values into the formula and calculate the monthly payment.P=1−(1+0.006583)−4819076×0.006583= 1−(1.006583)−48125.570308= 1−0.689567125.570308= 0.310433125.570308= $404.62