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8 months from now, your organization is planning to purchase new video conferencing equipment for a cost of $12,000. The equipment will have a useful life of 10 years and no salvage value. To pay for it, the organization plans to deposit $4,000 today in an investment account with an annual interest rate of 6.5%. In order to be able to purchase the equipment, the amount of additional money the organization must put in that investment account at the end of each month for 8 months is (select one): A. $1,536.79 B. $149.18 C. $533.90 D. $959.53 E. $42.09 F. $505.08

Respuesta :

Edufirst

Answer:

  • D. $959.53

Explanation:

1. Calculate how much money the $4,000 deposit today will be worth 8 months from now:

       [tex]Future\text{ }value=Deposit\times (1+i)^{(n)}[/tex]

Where:

  • Deposit = $4,000
  • i = monthly compound interest = 6.5% / 12 = 0.065/12
  • n = number of months (periods)

      [tex]Future\text{ }value=\$4,000\times (1+0.065/12)^{8}=\$4,176.66[/tex]

2. Calculate how much additioanl money you will need:

  • Cost of the equipment - Future value of deposit
  • $12,000 - $4,176.66 = $7,823.34

3. Calculate the amount of additional money the organization must put in that investment account, at the end of each month for 8 months, to produce $7,823.34 over the $4,176.66.

Use the formula for the future value, FV, of a constant periodic deposit, D, during n periods at the interest rate i:

    [tex]FV=D\times \bigg[\dfrac{(1+i)^n-1}{i}\bigg][/tex]

  • FV = $7,823.34
  • D = your unknown
  • i = 6.5% / 12 = 0.065/12
  • n = 8

      [tex]\$7,823.34=D\times \bigg[\dfrac{(1+(0.065/12))^8-1}{(0.065/12)}\bigg][/tex]

      [tex]\$7823.34=D\times 8.153320895\\\\\\D=\$959.53[/tex]

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