An accounting firm has ordered 55 new computers at a cost of \( \$ 1649 \) each. The machines will not be delivered for 8 months. What amount could the firm deposit today in an account paying \( 2.74 \% \) simple interest to have enough money to pay for the machines in 8 months? The present value PV of a future amount of FV dollars at a simple interest rate r for \( t \) years is given by which formula? A. \( \mathrm{PV}=\mathrm{rt}(1+\mathrm{FV}) \) B. PV \( =\mathrm{FV}(1+\mathrm{rt}) \) C. PV \( =\frac{\mathrm{FV}}{1+r t} \) D. PV \( =\frac{1+r t}{F V} \) The firm should deposit \( \$ \square \). (Round to the nearest cent as needed.)

To find out how much the accounting firm needs to deposit today, we first need to calculate the total cost of the computers. If each computer costs \( \$1649 \) and there are 55 computers, the future value (FV) is \( 55 \times 1649 = \$90,695 \). Now, to determine how much they should deposit today (PV), we use the formula \( \text{PV} = \frac{\text{FV}}{1 + rt} \). Here, \( r = 0.0274 \) (which is 2.74% expressed as a decimal), and \( t = \frac{8}{12} = \frac{2}{3} \) years. Plugging in the values gives us the necessary deposit. By plugging these into the formula, we calculate: \[ \text{PV} = \frac{90695}{1 + (0.0274 \times \frac{2}{3})} \approx \frac{90695}{1 + 0.01826667} \approx \frac{90695}{1.01826667} \approx 88940.56 \] The firm should deposit approximately \( \$88,940.56 \). Here’s a neat trick to remember: when dealing with present and future values, always convert your interest rate into decimal form, and break down your time into years to match the interest rate's timeline. It helps avoid mistakes that come from hasty calculations! For further context, this scenario reflects a common practice in financial planning where businesses strategize on capital investments. By understanding the concept of present value and future costs, firms can make better financing decisions, ensuring they have the funds ready when needed. Exploring financial literacy resources can deepen your grasp of these essential practices!