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Describe the effect an increase in n, the number of payment periods, has on the monthly payment P in the formula P = P V times StartFraction i over 1 minus (1 + i) superscript negative n Baseline EndFraction a. An increase in n, the number of payment periods, will not change P, the monthly payment. b. An increase in n, the number of payment periods, will create an increase in P, the monthly payment. c. An increase in n, the number of payment periods, will create a decrease in P, the monthly payment. d. An increase in n, the number of payment periods, can increase or decrease P, the monthly payment, depending on the value of PV.

Respuesta :

Edufirst

Answer:

  • Option b. An increase in n, the number of payment periods, will create an increase in P, the monthly payment.

Explanation:

The monthly payment formula described is:

[tex]P=PV\frac{i}{1-(1+i)^{-n}}[/tex]

Where:

  • P = monthly payment
  • PV = present value
  • i = interest rate per month
  • n = number of periods.

Mathematically, you can reason in the following way:

  • When n increases, the factor (1 +i)⁻ⁿ which is equal to the 1 / (1+ir)ⁿ decreases (because the denominator increases, the fraction increases).

  • When (1 + i)⁻ⁿ increases,  1 - (1 + i)⁻ⁿ decreases.

  • Since  1 - (1 + i)⁻ⁿ is in the denominator, when it decreases the fraction, which is equal to P, increases.

Thus, it is proved that an increase in n, the number of payment periods, will create an increase in P, the monthly payment (option b).

anthougo

The BEST description of the effect of an increase in n, the number of payment periods, on the monthly payment is c. An increase in n, the number of payment periods, will create a decrease in P, the monthly payment.

When the number of payment periods, n, increases, the monthly payment of the Liability will decrease instead of increasing, nor will it remain the same.

Thus, the BEST description of the effect of an increase in n, the number of payment periods, on the monthly payment is Option C.

Learn more about the payment period in an amortization schedule here: https://brainly.com/question/24576997

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