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baherus [9]
3 years ago
10

Steven wishes to save for his retirement by depositing $2,000 at the beginning of each year for thirty years. Exactly one year a

fter his last deposit, he wishes to begin making annual level withdrawals until he has made twenty withdrawals and used up the savings. Find the amount of each withdrawal if the effective interest rate is 3% during the first thirty years but only 2% after that.
Mathematics
1 answer:
Ad libitum [116K]3 years ago
8 0

Step-by-step explanation:

i = interest 3% for 30 years

This is a simple dynamical system for whom the the solutions are given as

S=R[\frac{(i+1)^n-1}{i}](i+1)

putting values we get

S=2000[\frac{(1.03)^{30}-1}{0.03}](1.03)

= $98005.35

withdrawal of money takes place from one year after last payment

To determine the result we use the present value formula of an annuity date

P = R\frac{1-(1+i)^{-n}}{i}{i+1}

we need to calculate R so putting the values and solving for R we get

R= $6542.2356

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marusya05 [52]

Answer:

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Step-by-step explanation:

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Read 2 more answers
segment BC is an are of a circle with radius 30.0 cm, and point P is at the center of curvature of the arc Segment DA is an arc
Elan Coil [88]

Answer:

The magnetic field is B = 3.87 *10^{-6} \ T

Direction is inward

 

Step-by-step explanation:

The diagram for this question is shown on the first uploaded image  

From the question we are told that

      The radius of  BC is  r_{BC} =  30 \ cm  =  0.30 \ m

      The radius of  DA is r _{DA} =  20 \ cm =  0.20 \ m

      The length of CD is  r_{CD} =  10 cm =  0.1 \ m

      The length of AB is  r_{AB} =  10 cm =  0.1 \ m

      The current is  I  =  11.4A

The magnetic field is mathematically represented as

      B =  B_{BC} +  B_{DA} + B_{CD} + B_{AB}

       B =  \frac{\mu_o I}{4 \pi } [ \frac{\theta_{DA}}{r_{DA}} + \frac{\theta_{BC}}{r_{BC}}+ \frac{\theta_{CD}}{r_{CD}}+\frac{\theta_{AB}}{r_{AB}}]

        Where

                 \theta_{BC} = \theta_{DA} =  \frac{2\pi}{3}

Where  \frac{2 \pi}{3}  =  120^o

                \theta_{CD} = \theta_{AB}  =  0^o

so

        B =  \frac{\mu_o I}{4 \pi } [ \frac{\frac{2\pi}{3} }{0.20} - \frac{\frac{2\pi}{3}}{0.30}}+ \frac{0}{0.10}+\frac{0}{0.10}]

         B = 3.87 *10^{-6} \ T

The direction is into the page

    This because the magnitude of the magnetic field due to arc BC whose direction is outward is less than that of DA whose direction is inward

This is because according to Fleming's Left Hand Rule  the direction of current is perpendicular to the direction of magnetic field so since  current in arc BC and DA are moving in opposite direction their magnetic field will also be moving in opposite direction

3 0
3 years ago
Least to greatest 1.5, 3.25, 1.66, 2.4
arsen [322]

Answer:

least to greatest

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6 0
3 years ago
If the density of a 35.cm3 block of wood is .85 g./ml calculate the woods mass.
Reil [10]
So the equation you're going to be using is mass = density x volume 
So the volume of your block is 35cm^3, and your density is .85g/ml 

so your equation would be 

mass=.85g/ml x 35cm^3 

your final answer is 29.75g/cm^3

Hope this helps :) 
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