Johnny opened a savings account 3 years ago. The account earns 7% interest, compounded continuously. If the current balance is $200.00, how much did he deposit initially? Round your answer to the nearest cent.
Answers
Answer: the initial deposit is $162.1
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
r = 7% = 7/100 = 0.07
t = 3 years
A= $200
Therefore,
200 = P x 2.7183^(0.07 x 3)
200 = P x 1.234
P = 200/1.234
P = $162.1 to the nearest cent
Related Questions
Complete the equation of the line through ( − 8 , 8 ) and ( 1 ,− 10 ). Use exact numbers.
HELP PLEASEEEE!!!!!!!
Molly and Arthur are taking their daughter Ginny on a roller coaster ride. For safety, they need to find their total weight before getting into the same car. Molly’s weight is MMM kilograms, Arthur’s weight is AAA kilograms, and Ginny’s weight is GGG kilograms.The expression (M+A)+G(M+A)+Gleft parenthesis, M, plus, A, right parenthesis, plus, G describes their total weight. We can also use the expression A+(G+M)A+(G+M)A, plus, left parenthesis, G, plus, M, right parenthesis to represent the same quantity.Match each amount in the situation with the expression that represents it.For reference:Molly is a female and an adult.Arthur is a male and an adult.Ginny is a female and a child.
Can you help me with this problem?
Answers
A thrift is a kind of bank that arranges mortgages (mostly for home ownership) and sets up accounts to receive deposits.
The statement is actually false. The difference is in who they can borrow from and whether or not they are set up for profit. Thrifts are usually non profit.
Answers
Answer:
11 ways
100 Pennies & 0 Dimes
90 Pennies & 1 Dimes
80 Pennies & 2 Dimes
70 Pennies & 3 Dimes
60 Pennies & 4 Dimes
50 Pennies & 5 Dimes
40 Pennies & 6 Dimes
30 Pennies & 7 Dimes
Step-by-step explanation:
Final answer:
There are 10 hundredths in one tenth. This can be understood by considering that a dime, representing one tenth of a dollar, is equivalent to 10 pennies, each penny representing one hundredth of a dollar.
Explanation:
In terms of decimals, one tenth is represented as 0.1 and a hundredth is represented as 0.01. Given this, there are 10 hundredths in one tenth (because 0.1 divided by 0.01 equals 10). To understand this using pennies and dimes, consider one dime (which represents one tenth of a dollar) and a penny (which represents one hundredth of a dollar). As there are 10 pennies in a dime, we can conclude that there are 10 hundredths in one tenth.
Learn more about Decimals here:
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B) 6 and 24
C) 9 and 39
D) 25 and 29
Answers
Answer C 9 and 39.
Let a the first and b the second
a=4b+3
a*b=351
==>b*(4b+3)=351
==>4b²+3b-351=0
Δ=9+4*4*351=5625=75²
==>b=(-3-75)/8 =-9.75 ==>a=4*(-9.75)+3=-36 (excluded) a>0
or b=(-3+75)/8=9 and a=4*9+3=39
Answers
3 is to 100 = 7.5 is to x
Rule: The product of the means equals the product of the extremes.
3•x = 7.5•(100)
3x = 750
x= 750 : 3
x = 250
A. Write the equations in slope-intercept form. (Show your work.)
B. Graph the pair of linear equations.
C. Use the graph to estimate the solution to the system of equations.
Help??
Answers
A. The first equation in slope-intercept form is y = -0.5x + 3. The second equation in slope-intercept form is y = 0.6x - 2.
B. The graph of the two equations is attached below.
C. The solution of the system of equation is (4.545,0.727)
A. To write the equations in slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept, we need to isolate "y" on one side of each equation.
1. 2x + 4y = 12
First, isolate "y" by subtracting 2x from both sides:
4y = -2x + 12
Next, divide both sides by 4 to get "y" by itself:
y = (-2x + 12) / 4
Simplify the equation:
y = -0.5x + 3
So, the first equation in slope-intercept form is y = -0.5x + 3.
2. 3x - 5y = 10
First, isolate "y" by subtracting 3x from both sides:
-5y = -3x + 10
Next, divide both sides by -5 to get "y" by itself:
y = (-3x + 10) / -5
Simplify the equation:
y = 0.6x - 2
So, the second equation in slope-intercept form is y = 0.6x - 2.
B. To graph the pair of linear equations, plot the y-intercept (where x = 0) and use the slope to find other points.
1. Graph the equation y = -0.5x + 3:
Plot the y-intercept at (0, 3).
Use the slope -0.5 to find another point; for example, if x = 2, then y = -0.5(2) + 3 = 2.
2. Graph the equation y = 0.6x - 2:
Plot the y-intercept at (0, -2).
Use the slope 0.6 to find another point; for example, if x = 3, then y = 0.6(3) - 2 = 0.
C. To estimate the solution to the system of equations, look for the point where the two lines intersect. This point represents the x and y values that satisfy both equations simultaneously. From the graph, we can interpret that the solution of the system of equation is (4.545,0.727)
To know more about equation:
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2x+4y=12
-2x -2x
4y=-2x+12
/4 /4
y=-1/2x+3
3x-5y=10
-3x -3x
-5y=-3x+10
/-5 /-5
y=3/5x-2
2) To graph SIF, you need to know what each aspect of the equation is. The formula is y=mx+b.
m stands for slope. A great way to remember it is rise/run (rise over run). Basically, the numerator in "m" is how far up you go to graph each point, and the denominator is how far left or right you go (remember, left is negative, right is positive). Let me give you an example. y=3/5x. In this formula, to graph each point, on the line, you'd go up 3, and to the right 5, then plot a point, then up 3, right 5, plot another one... you get it. What if the equation was y=3x though? The slope would be 3/1, or up 3, right one.
You know how to plot the points, but what coordinate do you startat? That's where the Y-Intercept comes into play. The Y-Intercept is basically where the line crosses the Y-axis. The b in the SIF formula is the y-intercept, and where you plot your very first coordinate on the line. If the SIF equation was y=1x+3, your first coordinate would be on the y axis, at an elevation of 3. Since the y-axis is at x=0, the coordinate would be (0,3).
3) Look at the graph now. Where do the lines cross? The x should be somewhere between 4 and 5, and the y is somewhere between 1.5 and 2. Therefor, your "estimation" should be something like (4.5,1.75)
I really hoped this helped you! It took a while to write so I'd appreciate if you'd choose the Brainliest answer -- thanks!
Answers
10x - speed on bike
v = s/t
s - distance
t - time
t = s/v
s₁ = 10 km
s₂ = 120 km
Solution:
Running speed = 5,5 km/h