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Phil purchased a car today at a price of $8,500. He paid $300 down in cash and financed the balance for 36 months at 5.75 percent, compounded monthly. What is the amount of each monthly loan payment

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Edufirst

Answer:

[tex]\large\boxed{\large\boxed{\$ 248.53}}[/tex]

Explanation:

The equation to calculate the monthly payment for fixed-rate loans is:

     [tex]Monthly\text{ }payment=Loan\times \bigg[\dfrac{r(1+r)^t}{(1+r)^t-1}\bigg][/tex]

Where:

  • Loan = $8500 - $300 = 8,200
  • r is the monthly interest = 5.75% / 12 = 0.0575/12 ≈ 0.00479
  • t is the number of moths = 36

Substituting:

[tex]Monthly\text{ }payment=\$8,200\times \bigg[\dfrac{(0.0575/12)(1+(0.0575/12))^{36}}{(1+(0.0575/12))^{36}-1}\bigg]=\$ 248.53[/tex]

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