g The owner of a small business borrowed $150,000 today (year 0) with an agreement to repay the loan with equal quarterly payments over a five year time period. If the interest rate is nominal 24% per year compounded quarterly, his loan payment each quarter is equal to:

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Answer:

[tex]\large\boxed{\large\boxed{\$13,077.68}}[/tex]

Explanation:

You have to use the equation to calculate the periodic payment, taking into account that the number of periods is four per year and the interest rate of the period is 24% divided by 4.

The formula is:

           [tex]Payment=Loan\times \bigg[\dfrac{r(1+r)^n}{(1+r)^n-1}\bigg][/tex]

Where:

  • n: total number of periods = 4 × 5 = 20
  • r: interest rate per period =24% / 4 = 6% = 0.06

Substitute and compute:

      [tex]Payment=\$150,000\times \bigg[\dfrac{0.06(1+0.06)^{20}}{(1+0.06)^{20}-1}\bigg]\\\\\\Payment=\$13,077.68[/tex]

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