Answer:
7%
Explanation:
It would grow by 7% each year which is the rate of return on stocks
The dimensions of the cylinder can be used to minimise cost of manufacture.
<h3>How to we find minimised cost?</h3>
Let's ignore the metal's thickness and assume that the material cost to manufacture is precisely proportionate to the surface area of a perfect cylinder.
A=2πr(r+h)
Given that V=1000=r2h and h=1000=r2, we can write
A=2πr(r+1000πr2)
A=2πr2+2000r−1
By setting the derivative to zero, we may determine the value of r that minimises A:
A′=4πr−2000r−2
0=4πr−2000r−2
2000r−2=4πr
2000=4πr3
r=500π−−−√3
r=5.419 + cm
h=1000πr2=10.838 + cm
The can with the smallest surface area has a volume of 1000 cm 3 and measures 5.419+ cm in radius and 10.838+ cm in height. The can has a surface area of 553.58 cm 2. Given a constant volume, the cylinder with diameter equal to height has the least surface area.
Can surface area (cm2) versus. radius (cm), where capacity = 1000cm 3.
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Answer:
Explanation:
The equation to calculate the <em>monthly payment</em> for fixed-rate loans is:
![Monthly\text{ }payment=Loan\times \bigg[\dfrac{r(1+r)^t}{(1+r)^t-1}\bigg]](https://tex.z-dn.net/?f=Monthly%5Ctext%7B%20%7Dpayment%3DLoan%5Ctimes%20%5Cbigg%5B%5Cdfrac%7Br%281%2Br%29%5Et%7D%7B%281%2Br%29%5Et-1%7D%5Cbigg%5D)
Where:
- Loan = $8500 - $300 = 8,200
- r is the monthly interest = 5.75% / 12 = 0.0575/12 ≈ 0.00479
- t is the number of moths = 36
Substituting:
![Monthly\text{ }payment=\$8,200\times \bigg[\dfrac{(0.0575/12)(1+(0.0575/12))^{36}}{(1+(0.0575/12))^{36}-1}\bigg]=\$ 248.53](https://tex.z-dn.net/?f=Monthly%5Ctext%7B%20%7Dpayment%3D%5C%248%2C200%5Ctimes%20%5Cbigg%5B%5Cdfrac%7B%280.0575%2F12%29%281%2B%280.0575%2F12%29%29%5E%7B36%7D%7D%7B%281%2B%280.0575%2F12%29%29%5E%7B36%7D-1%7D%5Cbigg%5D%3D%5C%24%20248.53)
The percentage of the disposable income that is discretionary is equal to 30.82% if the amount left after fixed expenses is $900.
As the amount left after payment of the fixed expenses is $900, this is said to be the discretionary income because discretionary income is equal to the disposable income minus fixed expenses.
Now we can calculate the percentage of disposable income that is discretionary as follows;
percentage of disposable income that is discretionary = (discretionary income ÷ disposable income) × 100
% discretionary income = (900 ÷ 2,920) × 100
% discretionary income = 90,000 ÷ 2,920
% discretionary income = 30.82%
Hence, 30.82% of the disposable income is calculated to be discretionary if the disposable income is $2,920 and the amount left after payment of fixed expenses is $900.
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Answer:
6.43%
Explanation:
The internal rate of return shall be determined by the Insurance firm using the following mentioned method:
Cash flows Year involved Present [email protected]% Present [email protected]%
($100) 1-20 ($851) ($1,487.75)
$3,310 20 $492 $1,832.67
($359) $344.92
IRR=A%+ (a/a-b)*(B%-A%)
A%=10% a= ($359) B%=3% b=$344.92
IRR=10%+(-$359/-$359-$344.92)*(3%-10%)
=6.43%
