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alexgriva [62]
3 years ago
14

Victor Vogel is 27 years old and currently earns $65,000 per year. He recently picked a winning number in the Wisconsin lottery.

After income taxes he took home $1,000,000. Victor put the entire amount into an account earning 5% per year, compounded annually. He wants to quit his job, maintain his current lifestyle and withdraw enough at the beginning of each year to replace his salary. At this rate, how long will the winnings last?
Got the explanation from classmates
N=??? I/Y=5 PV=1000000 PMT=-65000 FV=0
It will last 27 years.

Mathematics
1 answer:
Sonja [21]3 years ago
5 0

Answer:

  27 years

Step-by-step explanation:

The formula for the number of payments can be used:

  N = -log(1 +0.05(1 -1000000/65000))/log(1.05) +1 = 27.03

There will be a couple thousand dollars left after the 27th payment.

The winnings will last 27 years.

You might be interested in
A scale model of a tower is 24 inches tall and 18 inches wide. If the height of the actual tower is 60 feet, what is its width?
meriva

Answer:

The actual tower would be 45 ft wide.

Step-by-step explanation:

In order to find the width, we need to determine the scale factor. We can do that by dividing the actual height by the model height.

60ft:24in = 15ft:6in = 2.5ft:1in

Now we use that scale factor to determine the width. Multiply the scale factor by the width of the model.

18 inches * 2.5ft/in = 45 feet

6 0
2 years ago
How do you solve this?
solong [7]

It looks like your equations are

7M - 2t = -30

5t - 12M = 115

<u>Solving by substitution</u>

Solve either equation for one variable. For example,

7M - 2t = -30   ⇒   t = (7M + 30)/2

Substitute this into the other equation and solve for M.

5 × (7M + 30)/2 - 12M = 115

5 (7M + 30) - 24M = 230

35M + 150 - 24M = 230

11M = 80

M = 80/11

Now solve for t.

t = (7 × (80/11) + 30)/2

t = (560/11 + 30)/2

t = (890/11)/2

t = 445/11

<u>Solving by elimination</u>

Multiply both equations by an appropriate factor to make the coefficients of one of the variables sum to zero. For example,

7M - 2t = -30   ⇒   -10t + 35M = -150 … (multiply by 5)

5t - 12M = 115   ⇒   10t - 24M = 230 … (multiply by 2)

Now combining the equations eliminates the t terms, and

(-10t + 35M) + (10t - 24M) = -150 + 230

11M = 80

M = 80/11

It follows that

7 × (80/11) - 2t = -30

560/11 - 2t = -30

2t = 890/11

t = 445/11

4 0
2 years ago
Plz help!
jek_recluse [69]

Step-by-step explanation:

let's look at the last line :

x³ + 8x - 3 = Ax³ +5Ax + Bx² + 5B + Cx + D

since we find A, B, C, and D by simply comparing the factors of the various terms in x (or constants) in both sides of the equation, we need to combine a few terms on the right hand side (so that we have one term per x exponent grade).

x³ + 8x - 3 = Ax³ + (5A + C)x + Bx² + (5B + D)

by comparing now both sides, to make both sides truly equal, the factors have to be equal.

A = 1 (the same as for x³ on the left hand side).

B = 0 (a we have no x² on the left side).

5A + C = 8 (a 8 is the factor of x in the left side).

5×1 + C = 8

5 + C = 8

C = 3

5B + D = -3 (as the constant term is -3 on the left side).

5×0 + D = -3

D = -3

so, the 4th answer option is correct.

7 0
2 years ago
Which pair of angles are corresponding angles?<br><br> PLEASE HELP ME THIS IS DUE TMR
stiks02 [169]

Answer:

the answer is 3 and 7

Step-by-step explanation:

Angles formed when a transversal line cuts across two straight lines are known as corresponding angles. Corresponding angles are located in the same relative position, an intersection of transversal and two or more straight lines.

3 0
2 years ago
Solve for x. Please:)
lutik1710 [3]

Answer:

  x = 3

Step-by-step explanation:

The smaller triangle and larger one are similar, so corresponding sides are proportional.

  8/4 = (8 +(x -1))/5

  10 = x +7 . . . . . . . . . multiply by 5 and simplify

  3 = x . . . . . . . . . subtract 7

__

<em>Alternate solution</em>

The short segments are also proportional:

  (x -1)/(5 -4) = 8/4

  x -1 = 2 . . . . simplify

  x = 3 . . . . . . add 1

3 0
2 years ago
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