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Mark Stan elects to receive his retirement benefit over 20 years at the rate of 2,000 per month beginning one month from now. The monthly benefit increases by 5% each year. At a nominal interest rate of 6% convertible monthly, calculate the present value of the retirement benefit.

Respuesta :

jepessoa

Answer:

$419,253

Explanation:

we must find the present value of a growing annuity:

present value = [monthly payment / (i - g)] x [1 - [(1 + g)ⁿ x (1 + i)⁻ⁿ]

  • monthly payment = $2,000
  • i = (1 + 0.06/12)¹² - 1 = 0.061678 / 12 = 0.005139833
  • g = 5% / 12 = 0.004166667
  • n = 20 x 12 = 240

present value = [$2,000 / (0.00514 - 0.00416)] x [1 - [(1 + 0.00416)²⁴⁰ x (1 + 0.00514)⁻²⁴⁰] = $2,040,816 x [1 - (2.7083 x 0.293) = $2,040,816 x (1 - 0.794566) = $419,252.99 = $419,253

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