Question

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

Answer 1

Answer:

• D. $959.53

Explanation:

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

       $Future\text{ }value=Deposit\times (1+i)^{(n)}$

Where:

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

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

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:

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

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

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

      $\ 7823.34=D\times 8.153320895\\\\\\D=\ 959.53$