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anzhelika [568]
3 years ago
6

In your budget, you plan on putting a $3000 deposit on a car in 4 years. You currently have some extra money that you could put

into a savings account. If that savings account earns you 4% interest, compounded monthly, how much would you need to deposit today to have $2000 in 4 years?
Please show me proper work and give a good explanation on how you got your answer.
Mathematics
1 answer:
Elodia [21]3 years ago
6 0

Answer:

1704.74 = P

Step-by-step explanation:

The formula for compound interest is

A = P(1+r/n) ^nt  where

A is the amount in the account

P is the principle

r is the interest rate

n is the number of times the interest is compounded per year

t is the time in years

2000 = P (1+.04/12)^12*4

2000 = P (1.003333333)^48

Divide each side by (1.003333333)^48

2000/  (1.003333333)^48= P (1.003333333)^48/ (1.003333333)^48

1704.74110 = P

Rounding to the nearest cent

1704.74 = P

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The Campbell Company is considering adding a robotic paint sprayer to its production line. The sprayer's base price is $1,020,00
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1. The Year-0 net cash flow is -$1,061,500.

2. The net operating cash flows in Years 1, 2, and 3 are as follows:

Year 1: $288,750 ($386,000 x 1 - 0.25)

Year 2: $288,750 ($386,000 x 1 - 0.25)

Year 3: $288,750 ($386,000 x 1 - 0.25)

3. The additional Year-3 cash flow (i.e, the after-tax salvage and the return of working capital) is $468,750 {($599,000 x 1 - 0.25) + $19,500}.

4. The NPV of the project is ($13,139).

5. The machine should not be purchased because it does not yield a positive NPV.

<h3>What is the net present value?</h3>

The net present value (NPV) shows the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

It is determined by calculating the present values of cash flows using their present value factors as below:

<h3>Data and Calculations:</h3>

Initial cash outlay = $1,061,500 ($1,020,000 + $22,000 + $19,500)

Salvage value = $599,000

Increase in net working capital = $19,500

Annual savings before tax = $386,000

Tax rate = 25%

Annuial savings after tax = $288,750 ($386,000 x 1 - 0.25)

<h3>Determination of Net Present Value (NPV):</h3>

Year      Cashflows        PV Factor     Present Value

0          -$1,061,500               1             -$1,061,500

1              $288,750          0.901           $260,164

2             $288,750          0.812          $234,465

3             $288,750          0.731            $211,076

3             $468,750          0.731          $342,656

Net present value                                -$13,139

Thus, the project should not be undertaken by The Campbell Company due to the negative NPV that it yields.

Learn more about determining the NPV at brainly.com/question/18848923

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