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Select the correct answer.\newlineTaylor wants to purchase a car with an auto loan. He can get a 4848-month loan from his bank that is compounded monthly at an annual interest rate of 7.9%7.9\%. Suppose Taylor needs to obtain a loan for $1919,076076 to purchase the car. Use the formula for the sum of a finite geometric series to determine Taylor's approximate monthly payment. P=B,(0)1(1+0)48P=\frac{B,(0)}{1-(1+0)^{-48}} \newlineA). Taylor's approximate monthly payment for the loan will be $\$458458.3535. \newline B). Taylor's approximate monthly payment for the loan will be$\$464464.8181.\newlineC). Taylor's approximate monthly payment for the loan will be \newline$\$546546.5050.\newlineD). Taylor's approximate monthly payment for the loan will be $\$41324132.

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Q. Select the correct answer.\newlineTaylor wants to purchase a car with an auto loan. He can get a 4848-month loan from his bank that is compounded monthly at an annual interest rate of 7.9%7.9\%. Suppose Taylor needs to obtain a loan for $1919,076076 to purchase the car. Use the formula for the sum of a finite geometric series to determine Taylor's approximate monthly payment. P=B,(0)1(1+0)48P=\frac{B,(0)}{1-(1+0)^{-48}} \newlineA). Taylor's approximate monthly payment for the loan will be $\$458458.3535. \newline B). Taylor's approximate monthly payment for the loan will be$\$464464.8181.\newlineC). Taylor's approximate monthly payment for the loan will be \newline$\$546546.5050.\newlineD). Taylor's approximate monthly payment for the loan will be $\$41324132.
  1. Calculate Monthly Interest Rate: Calculate the monthly interest rate from the annual rate.\newlineAnnual interest rate = 7.9%7.9\%\newlineMonthly interest rate = 7.9%12\frac{7.9\%}{12}\newline= 0.6583%0.6583\%
  2. Convert to Decimal Form: Convert the monthly interest rate into decimal form for calculation.\newlineMonthly interest rate (decimal) = 0.6583100\frac{0.6583}{100}\newline= 0.0065830.006583
  3. 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.\newlineFormula: P=Bi1(1+i)nP = \frac{B \cdot i}{1 - (1 + i)^{-n}}\newlineWhere PP is the monthly payment, BB is the loan amount, ii is the monthly interest rate, and nn is the number of payments.\newlineB=$19,076B = \$19,076, i=0.006583i = 0.006583, n=48n = 48
  4. Calculate Monthly Payment: Plug the values into the formula and calculate the monthly payment.\newlineP=19076×0.0065831(1+0.006583)48P = \frac{19076 \times 0.006583}{1 - (1 + 0.006583)^{-48}}\newline= 125.5703081(1.006583)48\frac{125.570308}{1 - (1.006583)^{-48}}\newline= 125.57030810.689567\frac{125.570308}{1 - 0.689567}\newline= 125.5703080.310433\frac{125.570308}{0.310433}\newline= $404.62\$404.62

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