Use the number line to determine the unknown addend in the given number sentence.

A $7,600 par value bond sells for $7,373 . The coupon rate is 5.30% . What is the current yield

marta [7]

Answer:

Current yield = 5.46%

Step-by-step explanation:

Current yield is calculated by dividing the annual income (coupon) on the bond divided by the current price of the bond

Current yield = Annual coupon / Current price

In this case,

Face value or Par value = $7,600

Price of the bond = $7,373 (shows it is a discount bond since the price < FV)

Coupon rate = 5.30%

Next, calculate the Coupon payment in dollars;

Annual coupon PMT = Coupon rate * Face value

Annual coupon PMT = 0.053 * 7,600 = $402.8

Therefore, Current Yield = 402.8 / 7,373 = 0.05463

Current yield = 5.46%

5 0

4 years ago

Write the standard form of a line that passes through (1, 1) and (3, 4)

Sophie [7]

Answer:

3x - 2y = 1

Step-by-step explanation:

Step 1: Find the slope

slope m = (y2 - y1)(/x2 - x1)

m = (4 - 1)/(3 - 1) = 3/2

Step 1: Use the formula y = mx + b to solve

This is slope-intercept form of a line. We have a slope of 3/2, and a point (x, y), which is (1, 1). Plug those values into the equation above and solve for b (the only variable we are missing

1 = (3/2)(1) + b

1 = 3/2 + b

1 - 3/2 = b

2/2 - 3/2 = b

-1/2 = b

Step 2: Rewrite the formula using the slope and the b value we just calculated

y = (3/2)x - 1/2

Step 3: Standard form of a line is ax + by = c, where a is a positive integer, so we rearrange the equation from step 2 to standard form.

y = (3/2)x - 1/2

-(3/2)x + y = -1/2 (subtract (3/2)x from both sides)

-3x + 2y = -1 (multiply by 2 to get rid of the fraction on x)

3x - 2y = 1 (multiply by -1 so a becomes positive)

3 0

3 years ago

The Institute of Management Accountants (IMA) conducted a survey of senior finance professionals to gauge members’ thoughts on g

DochEvi [55]

Answer:

(1) The probability that the sample percentage indicating global warming is having a significant impact on the environment will be between 64% and 69% is 0.3674.

(2) The two population percentages that will contain the sample percentage with probability 90% are 0.57 and 0.73.

(3) The two population percentages that will contain the sample percentage with probability 95% are 0.55 and 0.75.

Step-by-step explanation:

Let X = number of senior professionals who thought that global warming is having a significant impact on the environment.

The random variable X follows a Binomial distribution with parameters n = 100 and p = 0.65.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of p if the following conditions are satisfied:

np ≥ 10
n(1 - p) ≥ 10

Check the conditions as follows:

$np= 100\times 0.65=65>10\\n(1-p)=100\times (1-0.65)=35>10$

Thus, a Normal approximation to binomial can be applied.

So, $\hat p\sim N(p, \frac{p(1-p)}{n})=N(0.65, 0.002275)$ .

(1)

Compute the value of $P(0.64$ as follows:

$P(0.64$

$=P(-0.20$

Thus, the probability that the sample percentage indicating global warming is having a significant impact on the environment will be between 64% and 69% is 0.3674.

(2)

Let $p_{1}$ and $p_{2}$ be the two population percentages that will contain the sample percentage with probability 90%.

That is,

$P(p_{1}$

Then,

$P(p_{1}$

$P(\frac{p_{1}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$P(-z$

The value of z for P (Z < z) = 0.95 is

z = 1.65.

Compute the value of $p_{1}$ and $p_{2}$ as follows:

$-z=\frac{p_{1}-p}{\sqrt{\frac{p(1-p)}{n}}}\\-1.65=\frac{p_{1}-0.65}{\sqrt{\frac{0.65(1-0.65)}{100}}}\\p_{1}=0.65-(1.65\times 0.05)\\p_{1}=0.5675\\p_{1}\approx0.57$ $z=\frac{p_{2}-p}{\sqrt{\frac{p(1-p)}{n}}}\\1.65=\frac{p_{2}-0.65}{\sqrt{\frac{0.65(1-0.65)}{100}}}\\p_{2}=0.65+(1.65\times 0.05)\\p_{1}=0.7325\\p_{1}\approx0.73$

Thus, the two population percentages that will contain the sample percentage with probability 90% are 0.57 and 0.73.

(3)

Let $p_{1}$ and $p_{2}$ be the two population percentages that will contain the sample percentage with probability 95%.

That is,

$P(p_{1}$

Then,

$P(p_{1}$

$P(\frac{p_{1}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$P(-z$

The value of z for P (Z < z) = 0.975 is

z = 1.96.

Compute the value of $p_{1}$ and $p_{2}$ as follows:

$-z=\frac{p_{1}-p}{\sqrt{\frac{p(1-p)}{n}}}\\-1.96=\frac{p_{1}-0.65}{\sqrt{\frac{0.65(1-0.65)}{100}}}\\p_{1}=0.65-(1.96\times 0.05)\\p_{1}=0.552\\p_{1}\approx0.55$ $z=\frac{p_{2}-p}{\sqrt{\frac{p(1-p)}{n}}}\\1.96=\frac{p_{2}-0.65}{\sqrt{\frac{0.65(1-0.65)}{100}}}\\p_{2}=0.65+(1.96\times 0.05)\\p_{1}=0.748\\p_{1}\approx0.75$