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2 years ago

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What lump sum of money must be deposited in a bank account at present time so that Php 500 monthly can be withdrawn for five yea

rs with the first withdrawal scheduled six years from today? Interest rate is 9% compounded quarterly.

1 answer:

jenyasd209 [6]2 years ago

3 0

Using compound interest, it is found that a sum of $16,586.26 must be deposited.

<h3>What is compound interest?</h3>

The amount of money earned, in compound interest, after t years, is given by:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

In which:

A(t) is the amount of money after t years.

P is the principal(the initial sum of money).

r is the interest rate(as a decimal value).

n is the number of times that interest is compounded per year.

t is the time in years for which the money is invested or borrowed.

In this problem:

We want to have Php 500 to be withdrawn monthly for 5 years, hence A(t) = 500 x 12 x 5 = 30000.

The first withdraw is 6 years from now, hence t = 6.

The interest rate is of r = 0.09.

Compounded quarterly, hence n = 4.

The amount deposited is the principal, hence:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

$30000 = P\left(1 + \frac{0.09}{4}\right)^{4(6)}$

$(1.025)^{24}P = 30000$

$P = \frac{30000}{(1.025)^{24}}$

$P = 16586.26$

A sum of $16,586.26 must be deposited.

To learn more about compound interest, you can take a look at brainly.com/question/25781328

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Carbon resistors often come as a brown cylinder with colored bands. These colored bands can be read to determine the manufacture

alexandr1967 [171]

Answer:

a) 4.7 kΩ, +/- 5%

b) 2.0 MΩ, +/- 20%

Explanation:

a) If the resistor has the following combination of color bands:

1) Yellow = 1st digit = 4

2) Violet = 2nd digit = 7

3) Red = multiplier = 10e2

4) Gold = tolerance = +/- 5%

this means that the resistor has 4700 Ω (or 4.7 kΩ), with 5% tolerance.

b) Repeating the process for the following combination of color bands:

1) Red = 1st digit = 2

2) Black = 2nd digit = 0

3) Green = multiplier = 10e5

4) Nothing = tolerance = +/- 20%

This combination represents to a resistor of 2*10⁶ Ω (or 2.0 MΩ), with +/- 20% tolerance.

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3 years ago

What is a p-n junction? Show by the diagram.

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Answer:

The p-n junction is a region formed when a p -type semiconductor material is joined to an n-type semiconductor material

Explanation:

The p type semiconductor has holes as its majority charge carriers making it positively charged while the n –types has an overall negative charge. At the junction the holes move towards the electron until such a time when there is a balance in charges from both materials, which leads to the formation of the depletion zone as shown in the attachment below

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3 years ago

Gray cast iron, with an ultimate tensile strength of 31 ksi and an ultimate compressive strength of 109 ksi, has the following s

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Using an appropriate failure theory, find the factor of safety in each case. State the name of the theory that you are using the theory is max stress theory.

<h3>Wat is the max stress theory?</h3>

The most shear strain concept states that the failure or yielding of a ductile fabric will arise whilst the most shear strain of the fabric equals or exceeds the shear strain fee at yield factor withinside the uniaxial tensile test.”

Stress states at various critical locations are f= 2.662.

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1. A glass window of width W = 1 m and height H = 2 m is 5 mm thick and has a thermal conductivity of kg = 1.4 W/m*K. If the inn

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Answer:

1. $\dot Q=19600\ W$

2. $\dot Q=120\ W$

Explanation:

1.

Given:

height of the window pane, $h=2\ m$

width of the window pane, $w=1\ m$

thickness of the pane, $t=5\ mm= 0.005\ m$

thermal conductivity of the glass pane, $k_g=1.4\ W.m^{-1}.K^{-1}$

temperature of the inner surface, $T_i=15^{\circ}C$

temperature of the outer surface, $T_o=-20^{\circ}C$

<u>According to the Fourier's law the rate of heat transfer is given as:</u>

$\dot Q=k_g.A.\frac{dT}{dx}$

here:

A = area through which the heat transfer occurs = $2\times 1=2\ m^2$

dT = temperature difference across the thickness of the surface = $35^{\circ}C$

dx = t = thickness normal to the surface = $0.005\ m$

$\dot Q=1.4\times 2\times \frac{35}{0.005}$

$\dot Q=19600\ W$

2.

air spacing between two glass panes, $dx=0.01\ m$

area of each glass pane, $A=2\times 1=2\ m^2$

thermal conductivity of air, $k_a=0.024\ W.m^{-1}.K^{-1}$

temperature difference between the surfaces, $dT=25^{\circ}C$

<u>Assuming layered transfer of heat through the air and the air between the glasses is always still:</u>

$\dot Q=k_a.A.\frac{dT}{dx}$

$\dot Q=0.024\times 2\times \frac{25}{0.01}$

$\dot Q=120\ W$

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3 years ago

A motor car shaft consists of a steel tube 30 mm internal diameter and 4 mm thick. The engine develops 10 kW at 2000 r.p.m. Find

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The maximum shear stress in the tube when the power is transmitted through a 4: 1 gearing is 28.98 MPa.

<h3>What is power?</h3>

Power is the energy transferred per unit time.

Torque is find out by

P = 2πNT/60

10000 = 2π x 2000 x T / 60

T =47.74 N.m

The gear ratio Ne / Ns =4/1

Ns =2000/4 = 500

Ts =Ps x 60/(2π x 500)

Ts =190.96 N.m

Maximum shear stress τ = 16/π x (T / (d₀⁴ - d₁⁴))

τ max =T/J x D/2
where d₁ = 30mm = 0.03 m

d₀ = 30 +(2x 4) = 38mm =0.038 m

Substitute the values into the equation, we get

τ max = 16 x 190.96 x 0.038 /π x (0.038⁴ - 0.03⁴)

τ max = 28.98 MPa.

Thus, the maximum shear stress in the tube is 28.98 MPa.

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2 years ago