A consol paying $20 annually when the interest rate is 5 percent has a price of

1 answer:

8 0

Answer: $ 400 .
_________________________
Explanation:
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Note that a "consol" is a "perpetuity".
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To find the "PV" (Present Value) of a perpetuity, we use the equation: PV = C / r = Current value / interest rate

= $20 / (5%) = $20 / (5/100) = $20 / (0.05) = $400 .
___________________________________________________

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Assume that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles

OverLord2011 [107]

Answer:

Final answer is approx 6.644 years.

Step-by-step explanation:

Given that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year.

So we can use growth formula:

$A=P\left(1+r\right)^t$

Then we get equation for motorcycles and cars as:

$A=5.75\left(1+0.16\right)^t$

$A=3.5\left(1+0.25\right)^t$

Now we need to find about when the sale of cars will be more than the sale of motorcycles. So we get:

$3.5\left(1+0.25\right)^t>5.75\left(1+0.16\right)^t$

$3.5\left(1.25\right)^t>5.75\left(1.16\right)^t$

$\frac{\left(1.25\right)^t}{\left(1.16\right)^t}>\frac{5.75}{3.5}$

$\left(\frac{1.25}{1.16}\right)^t>1.64285714286$

$t\cdot\ln\left(\frac{1.25}{1.16}\right)>\ln\left(1.64285714286\right)$

$t>\frac{\ln\left(1.64285714286\right)}{\ln\left(\frac{1.25}{1.16}\right)}$

$t>6.6436473051$

Hence final answer is approx 6.644 years.

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3 years ago

This writing prompts is hard

Solnce55 [7]

A.) Simplifying the equation would lead you to 15x^2-3x+9

b.) You know your answer is correct because you're adding the two polynomials together. 9x^2+6x^2 is 1tx^2. Now you have 2x-5x and since the negative is bigger, you get -3x. Then 5+4 is 9. You have no like terms therefore your answer is 15x^2-3x+9

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3 years ago

Heidi takes 45 minutes to cover a distance of 5.4 miles on a treadmill. Find the average distance covered by Heidi in one minute

Natali5045456 [20]

Heidi goes 0.12 miles a minute

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3 years ago

The population of deer in a state park in 1985 was 46,000. The population in 1990 was 72,000. What is the rate of change of the

Vesnalui [34]

Answer:

5200 deer/year

Step-by-step explanation:

$rateofchange=changeinpopulation \div changeinyears$
we will call the rate of change, the slope of the function
$slope=(72000-46000)deer\div (1990-1985)years\\=26000deer\div 5years\\=(\frac{26000}{5}) deer/year\\==5200deer/year$