Answer:
- <u>The rate of return is 8.15%</u>
- <u>This is a good investment</u>
<u></u>
Explanation:
For the first question, you need to find the rate that makes the present value of a stream of ten constant annual payments of $15,000 equal to the $100,000 investment.
The formula that returns the present value of a constant payment is called the annuity formula and is:
![Present\text{ }value=payment\times \bigg[\dfrac{1}{r}-\dfrac{1}{r(1+r)^t}\bigg]](https://tex.z-dn.net/?f=Present%5Ctext%7B%20%7Dvalue%3Dpayment%5Ctimes%20%5Cbigg%5B%5Cdfrac%7B1%7D%7Br%7D-%5Cdfrac%7B1%7D%7Br%281%2Br%29%5Et%7D%5Cbigg%5D)
In your problem you know:
- Present value: $100,000
- payment: $15,000
- r: ?
- t: 10
You cannot solve for r directly. You must guess a value and calculate the right side of the equation until to you find the rate that makes it equal to 100,000.
Try 5%:
![\$15,000\times \bigg[\dfrac{1}{0.05}-\dfrac{1}{0.05(1+0.05)^{10}}\bigg]=\$115,826](https://tex.z-dn.net/?f=%5C%2415%2C000%5Ctimes%20%5Cbigg%5B%5Cdfrac%7B1%7D%7B0.05%7D-%5Cdfrac%7B1%7D%7B0.05%281%2B0.05%29%5E%7B10%7D%7D%5Cbigg%5D%3D%5C%24115%2C826)
Then, the rate of return is greater than 5%. After several trials you will find that the rate of return is 8.15%.
Since this rate is higher than 8%, which is what the company requires, this is a good investment.
Answer:y= -4
Step-by-step explanation:
1 Solve for xx in 7x-4y=-127x−4y=−12.
x=\frac{4(y-3)}{7}
x=
7
4(y−3)
2 Substitute x=\frac{4(y-3)}{7}x=
7
4(y−3)
into 9x-4y=-209x−4y=−20.
\frac{36(y-3)}{7}-4y=-20
7
36(y−3)
−4y=−20
3 Solve for yy in \frac{36(y-3)}{7}-4y=-20
7
36(y−3)
−4y=−20.
y=-4
y=−4
4 Substitute y=-4y=−4 into x=\frac{4(y-3)}{7}x=
7
4(y−3)
.
x=-4
x=−4
5 Therefore,
\begin{aligned}&x=-4\\&y=-4\end{aligned}
x=−4
y=−4
Surface area of square pyramid having square base side = 10 cm and slant height = 20 cm is 340 square meters
<u>Solution:</u>
Given that
Shape of the roof is square pyramid.
Base length of square pyramid roof = 10 meters
Slant height of square pyramid roof = 12 meters
Need to calculate the surface area of the roof
Where s is side of square base and l is slant height.
In our case s = 10 meters and l = 12 meters
On substituting the given values in formula we get
Surface area of square pyramid 
Hence surface area of square pyramid having square base side = 10 cm and slant height = 20 cm is 340 square meters.
Answer:
2(w+6)
Step-by-step explanation:
