Cameron opens a checking account and a savings account at his local bank. He deposits $10,000 into his checking account and $2,000 into his savings account. He will withdraw $1,200 from his checking account each year. His savings account earns 8% interest each year. In how many years will both accounts have the same balance?

Answers

Answer 1

Answer: The correct answer is:
5.9 years.

Explanation:
Let x be the number of years. For the checking account, our expression would be 10000-1200x, since he withdraws $1200 from his account each year, and he begins with $10,000.

The formula for simple interest is:
I=prt
where:
p is the principal, r is the rate and t is the time

using our information, we have
p=2000,
r=8%=8/100=0.08, and
t=x.

This gives us 2000(0.08)(x).
However, we must add the $2000 to this (interest is added on to the principal); this gives us:
2000+2000(0.08)(x).

Setting these two equal, we have:
10000-1200x = 2000+2000(0.08)(x).

Simplifying the right hand side, we have:
10000-1200x=2000+160x.

Add 1200x to both sides:
10000-1200x+1200x=2000+160x+2000x;
10000=2000+1360x.

Subtract 2000 from both sides:
10000-2000=2000+1360x-2000;
8000=1360x.

Divide both sides by 1360:
$(8000)/(1360) = (1360x)/(1360)$ ;
5.9=x.

Answer 2

Answer:

Let x be the number of needed years.

1. He deposits $10,000 into his checking account and he will withdraw $1,200 from his checking account each year. Then after x years he will have $10,000-$1,200x in his checking account.

2. He deposits $2,000 into his savings account and his savings account earns 8% interest each year, then after x years he will have $\$2,000\cdot (1.08)^x.$

3. Equate these amounts of money:

$10,000-1,200x=2,000\cdot (1.08)^x.$

4. Solve this equation:

divide the equation by 400:

$25-3x=5\cdot (1.08)^x;$

plot graphs of the function $y=25-3x$ and $y=5\cdot (1.08)^x$ (see attached diagram);
find the common point of these two graphs: (6.663,5.01).

Conclusion: he needs nearly 6.663 years.

Related Questions

The area of a rectangular garden in square feet is x^2+35x-450. The width is (x-10) feet. What is the length of the garden?
Two lines have given equations. At what point do they intersect? 2x-y=1 3x=y-6
What is the equation of the line that passesthrough the points (3,-1) and (7, 3)?
Shalika bought a purse for $120. The tax rate is 9%. Which proportion can be used to find the amount of tax Shalika will pay? A.9/120=x/100 B.120/x=100/9 C.x/120=100/9 D.120/9=100/x
the Pentagon in Washington DC is immense in size with an outside wall 921 feet length what is the perimeter of the Pentagon

Use backtracking to find a subset, if it exists, of the set {27, 24, 19, 14, 11, 8} with sum:a) 20
b)60

Answers

Its A. 20 because most of the numbers in the set are closest to 20 or a little below 20

Is it possible to draw a triangle with sides 150cm, 10cm, 10cm

Answers

It is absolutely impossible to draw a triangle of sides 150 , 10 and 10 cm. With one side so large, it is impossible, which will make the two angles two small to intersect and the angle will be < 0, which is not possible in a triangle.

Nine minus the quotient of two and a number x.

Answers

Answer:

9 - ( 2 ÷ x )

Step-by-step explanation:

How many integers exist for the value of n such that n²-19n+91 is perfect square?

Answers

one because then it would be (ax+b)^2=cx^2+dx+e if cx^2+dx+e is a perfect square

4a² - 25? little help? Can you show me the steps to gets the answer? Thanks!

Answers

4a² - 25

= (2a)² - 5²

= (2a+5)(2a-5) since a² -b² = (a+b)(a-b)

This is simply a difference of squares. To factor this, you simply take the square roots of the leading coefficient and the C term. Thus you get 2 and 5. As a pair of factors, it is simply (2a+5)(2a-5). If you actually need to solve this, you can set either the factors or the original equation equal to 0.

What is the slope of a line perpendicular to x - 5y = -10?What is the slope of a line parallel to 4x + y = -1?

What is the slope of a line perpendicular to x - 3y = 9?

What is the slope of a line parallel to 10x - 5y = 8?

What is the slope of a line parallel to 4x + 2y = 5?

Answers

slope of line perpendicular to : x - 5y = -10
-5y = -x - 10
y = 1/5x + 2.....slope here is 1/5...perpendicular line needs a negative reciprocal slope. All that means is flip the slope and change the sign.
1/5......flip.....5/1.....change the sign....-5/1...or just -5 <== answer

slope of line parallel to 4x + y = -1
y = -4x - 1...slope here is -4....parallel lines will have the same slope
answer is : -4

slope of line perpendicular to x - 3y = 9
-3y = -x + 9
y = 1/3x - 3....slope = 1/3.....flip...3/1....change sign...-3 <== answer

slope of line parallel to 10x - 5y = 8
-5y = -10x + 8
y = 2x - 8/5....slope = 2....parallel lines have same slope...answer = 2

slope of line parallel to 4x + 2y = 5
2y = -4x + 5
y = -2x + 5/2.....slope = -2

y=-4x would be parallel to 4x + y = -1

y=-3x would be perpendicular to x - 3y = 9

y=-2x would be parallel to 10x - 5y = 8

y=2x would be parallel to 4x + 2y = 5

Other Questions

What is √49 times 7?

Correctly complete the square for the equation belowx2 - 5x = 0

Marina saved $80 from her babysitting job. She wants to buy some shirts and pants that are on sale at her favourite store for $17 each. How many items of clothing can she buy?

Marcia will make a frame for her picture the length of the picture is 15 inches the width is one third of the length how much wood does marcia need for