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notsponge
2 months ago
9

The Distribution Point plans to save $2,000 a month for the next 3 years for future emergencies. The interest rate is 4.5 percen

t compounded monthly. The first monthly deposit will be made today. What would today's deposit amount have to be if the firm opted for one lump sum deposit that would yield the same amount of savings as the monthly deposits after 3 years?
Business
1 answer:
stepan [3.5K]2 months ago
5 0

Answer:

Today's deposit of 36,922.02 dollars corresponds to a sequence of emergency deposits amounting to 2,000 starting from today.Explanation:

To determine the equivalent lump sum, we calculate the future value of the emergency deposits. Given that the deposits are made at the beginning, it qualifies as an annuity-due:

C 2,000

time      36 (3 years x 12 months per year)C \times \frac{(1+r)^{time} -1}{rate}(1+r) = FV\\

rate 0.045

FV $180,082.6885

Next, we compute the present value that yields this total: 2000 \times \frac{(1+0.045)^{36} -1 }{0.045}(1+0.045) = FV\\

Maturity  $180,082.6885

time   36.00

rate  0.045

\frac{Maturity}{(1 + rate)^{time} } = PV

PV   36,922.02

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Scilla [3833]

Response:

-11.8%

Clarification:

to resolve this problem, it's important to keep in mind that a bond's worth is primarily determined by figuring out the present value of its cash flow sequence. Therefore, consider a bond in terms of you being the creditor; you would earn interest from the loaned amount (the coupon), and after n years, you'd receive back the initial amount lent (the principal). Applying the relevant formula, we get the value of the bond as follows:

price=\frac{principal*coupon}{(1+i)^{1} }+ \frac{principal*coupon}{(1+i)^{2} } \frac{principal*coupon}{(1+i)^{3} }+...+\frac{principal+principal*coupon}{(1+i)^{n} }

in this specific scenario, there are 29 years left until it matures after one year, thus we have:

price=\frac{1,000*0.04}{(1+0.08)^{1} }+ \frac{1,000*0.04}{(1+0.08)^{2} } \frac{1000*0.04}{(1+0.08)^{3} }+...+\frac{1,000+1,000*0.04}{(1+0.08)^{30} }

price=553.6638

given that the interest rate is higher, the return on the investment is as follows:

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4 0
2 months ago
Explain why the practice described in the following scenario is NOT sustainable. There has recently been high demand for wheat a
Nady [3600]
I perceive this method as unsustainable for two main reasons. Initially, from an agricultural standpoint, I believe it's imprudent to cultivate the same crop in a field for four consecutive years; crop rotation is preferable to prevent nutrient depletion from the soil. Secondly, from an economic viewpoint, it might be unwise as the farmer is putting everything at risk by assuming that wheat prices will remain high, whereas having a variety of crops could provide alternatives in case of a fall in wheat prices.
3 0
2 months ago
Read 2 more answers
to calculate your monthly lease payment on a three-year lease using the "residual value" of a $26,500 MSRP car, subtract the 48%
marusya05 [3725]

Answer:

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Explanation:

In this case, we aim to determine the estimated monthly payment for a lease of 3 years, and the question outlines the steps involved.

To start, we take the MSRP and deduct the residual value of 48%

Calculating 48% of $26,500 gives us 48/100 * 26,500 = $12,720

We then subtract this value from $26,500

This results in $26,500 - $12,720 = $13,780

With a duration of 3 years, that translates to 36 months

Thus, the estimated monthly payment can be calculated as;

$13,780 / 36 = 382.7777777777778 which rounds to approximately $383

6 0
2 months ago
chandler Communications'CFO has provided the following information: The company's capital budget is expected to be $5,000,000. T
harina [3808]

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= 30/100 × $5,000,000

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= $4,500,000 - $1,500,000

= $3,000,000

5 0
2 months ago
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