Nathaniel invested $37,000 in an account paying an interest rate of 5.7% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $70,900?
Answer:
11
Step-by-step explanation:
\text{Compounded Daily:}
Compounded Daily:
A=P\left(1+\frac{r}{n}\right)^{nt}
A=P(1+
n
r
)
nt
Compound interest formula
A=70900\hspace{35px}P=37000\hspace{35px}r=0.057\hspace{35px}n=365
A=70900P=37000r=0.057n=365
Given values
70900=
70900=
\,\,37000\left(1+\frac{0.057}{365}\right)^{365t}
37000(1+
365
0.057
)
365t
Plug in values
70900=
70900=
\,\,37000(1.0001562)^{365t}
37000(1.0001562)
365t
Simplify
\frac{70900}{37000}=
37000
70900
=
\,\,\frac{37000(1.0001562)^{365t}}{37000}
37000
37000(1.0001562)
365t
Divide by 37000
1.9162162=
1.9162162=
\,\,1.0001562^{365t}
1.0001562
365t
\log\left(1.9162162\right)=
log(1.9162162)=
\,\,\log\left(1.0001562^{\color{blue}{365t}}\right)
log(1.0001562
365t
)
Take the log of both sides
\log\left(1.9162162\right)=
log(1.9162162)=
\,\,\color{blue}{365t}\log\left(1.0001562\right)
365tlog(1.0001562)
Bring exponent to the front
\frac{\log\left(1.9162162\right)}{\log\left(1.0001562\right)}=
log(1.0001562)
log(1.9162162)
=
\,\,\frac{365t\log\left(1.0001562\right)}{\log\left(1.0001562\right)}
log(1.0001562)
365tlog(1.0001562)
Divide both sides by log(1.0001562)
4164.8632402=
4164.8632402=
\,\,365t
365t
Use calculator
\frac{4164.8632402}{365}=
365
4164.8632402
=
\,\,\frac{365t}{365}
365
365t
Divide by 365
11.4105842=
11.4105842=
\,\,t
t
t\approx
t≈
\,\,11
11
Using compound interest, it is found that it would take 11 years for the value of the account to reach $70,900.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
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.Hence, the parameters are given as follows:
[tex]A(t) = 70900, P = 37000, n = 365, r = 0.057[/tex]
We have to solve for t, then:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]70900 = 37000\left(1 + \frac{0.057}{365}\right)^{365t}[/tex]
[tex]\left(1 + \frac{0.057}{365}\right)^{365t} = \frac{70900}{37000}[/tex]
[tex]\left(1 + \frac{0.057}{365}\right)^{365t} = 1.91621622[/tex]
[tex](1.00015616)^{365t} = 1.91621622[/tex]
[tex]\log{(1.00015616)^{365t}} = \log{1.91621622}[/tex]
[tex]365t\log{1.00015616} = \log{1.91621622}[/tex]
[tex]t = \frac{\log{1.91621622}}{365\log{1.00015616}}[/tex]
t = 11.41
Rounding to the nearest year, it would take 11 years for the value of the account to reach $70,900.
More can be learned about compound interest at https://brainly.com/question/25781328
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HELPPPPPPP I WILLL GIVE THE BRAINLIESTTTTTTTTTTTT
At Open Skate Night, admission is $4.50 with a membership card and $5.00 without a membership card. Skate rentals are $2.00.
Aidan paid the admission for himself and two friends at Open Skate Night. Aidan had a membership card, but his friends did not. Aidan paid with a $20 bill. How much change should Aidan receive?
Aidan should receive
$_________ in change.
Answer:
50 cents
Step-by-step explanation:
4.50 + 5.00 + 5.00 + 2.00 x 3 = ?
^
20.00 - ?
Angie uses the equation E=0.03s + 25,000 to find her yearly earning E based on her total sales s. What is the independent variable
Answer:
25000
Step-by-step explanation:
it's independent because it's not related with her total sales s
The quotient of a number and (-3) is (-80) Find the number.
Answer:
240
Step-by-step explanation:
Solve for g.
18 = 3(g + 19)
Which of these transformations occurs when the blades of a fan turn?
a. dilation
b. reflection
c. rotation
d. translation
QUICK WHAT IS 3 2/5X 2 1/3
Answer: 119/15 = 7 14/15
PLEASE HELP!!! GIVING BRAINLIST
If x + 2y = 8 and x/2 -y= 10, then x = ?
A)-3
B) 0
C) 10
D) 14
Answer:
D. 14
make y the subject of the formula in equation 1 and then substitute it in equation 2
what is 100 times 7 plus 23
100 times 7= 700 any number times 100 you would add two zeros, 700+23=723
Hope this helps :]
what is 2/3 divided by 1/2 in fractions
Answer:
4/3
Step-by-step explanation:
Answer:
the answer is 4/3
Step-by-step explanation:
Hope that helps!
The graph shows the volume of water in a sink, x minutes after the faucet is turned on.
Answer:
Conner is correct.
Step-by-step explanation:
Answer:
Connor is correct because the rate of water flowing is equal to the slope. Water is flowing at a rate that is equal to 2 gallons per minute.
Step-by-step explanation:
A person can pay $9 for a membership to the history museum and then go to the museum for just $1 per visit. For a member of the history museum, what is the total cost of 23 visits?
Answer:
$32Step-by-step explanation:
Step one:
Given that membership is $9 and the cost per visit is $1
let the number of visits be x
and the total cost be y
the total cost for the situation is modeled as
y=mx+c-----equation of a line
Step two:
given that x=23, we can solve for the totals cost as
by substituting we have
y=1*23+9
y=23+9
y=32
The total cost for 23 visits is $32
A distrubutor wants to make 1,000 pounds of trail mix that is 8% raisins. He will use a mix that is 5% raisins and a mix that is 20% raisins. How many pounds of each should he use?
Answer:
He should use 800 pounds of trail mix 5% raisins and 200 pounds of trail mix 20% raisins
Step-by-step explanation:
System of Equations
Let's call
x = pounds of trail mix 5% raisins
y = pounds of trail mix 20% raisins
The distributor wants to make 1,000 pounds of trail mix, thus:
x + y = 1,000 [1]
The mix must be 8% raisings as a combination of x and y, thus:
5x + 20y = 8*1,000 = 8,000
Dividing by 5:
x + 4y = 1,600 [2]
Subtracting [2] and [1]:
4y - y = 1,600 - 1,000
Operating:
3y = 600
y = 200
From [1]
x = 1,000 - y = 1,000 - 200
x = 800
He should use 800 pounds of trail mix 5% raisins and 200 pounds of trail mix 20% raisins
Answer:
5% raisin mix: 800 lbs
20% raisin mix: 200 lbs
Step-by-step explanation:
Let number of 5% be x; and number of 20% be a.
x + y = 1000
5% · x + 20% · y = 8% of 1000 pounds
0.05x + 0.2y = 80
x = 1000 - y
0.05(1000 - y) + 0.2y = 80
50 - 0.05y + 0.2y = 80
0.15y = 30
y = 200
x = 1000 - y
x = 1000 - 200
x = 800
Which graph is the solution to the inequality below?
Answer:
it the third answer
Step-by-step explanation:
3(x-5)< 5x+7
x>-11Asappppp , pls help me :((
Answer:
Not a function
Step-by-step explanation:
This is not a function because every x value has more than one y value. Think about it this way. If you have a person and you are telling them to go to three different places at once, they can't. That means this isn't a function. Hope this helps!
Answer: That is not a function
Hope it helped
Step-by-step explanation:
Find the equation of a parabola that has a vertex of (3,7) and contains the point (-2,-6)
Answer:
Step-by-step explanation:
What is the equation of the line in the graph?
Answer:
Step-by-step explanation:
Equations and Inequalities One-Pager
NEED ANSWER ASAP PLEASE HELP!!!
What composition of transformations is equivalent to a rotation of 180°?
Open-ended question
Answer:
90 is correct good job
Step-by-step explanation:
A = p + prt solve for t
Answer:
t = [tex]\frac{A - p}{pr}[/tex]
Step-by-step explanation:
A = p + prt
A - p = p - p + prt
A - p = 0 + prt
A - p = prt
[tex]\frac{A - p}{pr}[/tex] = [tex]\frac{prt}{pr}[/tex]
[tex]\frac{A - P}{pr}[/tex] = t
Identify all segments that are parallel to XY
A. ST
B. VZ, VW, ST
C. QR, QU
D. VW
Answer:
a. ST
Step-by-step explanation:
Compare the two statements below and decide if the phrase: "In a plane," needs to be included in order to make a true statement.
1. In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.
versus
2. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.
answer choices:
A) It does not need to be included. By leaving it out of the statement, the reader considers three dimensions not just the xy-plane. The two parallel lines would determine a plane. However, the transversal could intersect only one of the lines. This would allow the proof to use the Corresponding Angles Theorem.
B) It does not need to be included. By leaving it out of the statement, the reader considers three dimensions not just the xy-plane. The two parallel lines would determine a plane. However, the transversal could intersect only one of the lines. This would allow the proof to use the Angle Bisector Theorem.
C) It needs to be included as it forces the reader to consider only two dimensions, like the xy-plane. The two parallel lines would determine the plane and the transversal would intersect both lines. This would allow the proof to use the Corresponding Angles Theorem.
D) It needs to be included as it forces the reader to consider only two dimensions, like the xy-plane. The two parallel lines would determine the plane and the transversal would intersect both lines. This would allow the proof to use the Angle Bisector Theorem.
by any chance do you go to a higl school in Conroe bc I’m taking that exact test on canvas
Step-by-step explanation:
True or False
If an acute angle is 80o then we add the obtuse angle of 110o to equal 180o?
Answer:
true
Step-by-step explanation:
30 points!!!!!!!!!!!!!!!!!!!!!!! Help ASAP!!! 1.) Line a passes through points (-2, 1) and (2, 9). Write an equation in slope intercept form that is parallel to line a.
Step 1: Use slope formula* to determine slope (or m) using both points given.
[tex]\frac{9 - 1}{2 - (-2)}\\\\\frac{8}{4} = 2[/tex]
Step 2: Use slope-intercept formula** , ONE of the points given, and the slope we just found to solve for b.
[tex]1 = 2(-2) + b\\\\1 = -4 + b\\\\5 = b[/tex]
Step 3: Now we can set up an equation of this line in slope-intercept form.
[tex]y = 2x + 5[/tex]
*Slope formula: y₂ - y₁/x₂ - x₁
**Slope-intercept formula: y = mx + b
Answer:
The slope calculator helps find the slope of any line through two given points. ... To find the equation of a line for any given two points that this line passes through, use our ... to calculate the slope of the line passing through the points (3,8) and (-2, 10) . ... Make sure that the points you measure from are the same as step 1.
Step-by-step explanation:
Please help me nobody will help me with this please
Answer:
[tex]24[/tex]
Step-by-step explanation:
Each bottle of water costs $2 so we multipy 12 by 2.
[tex]12[/tex]×[tex]2=24[/tex]
Find the ratios x:y:z if x:y=9:10 and y:z=5:3
Answer:
Step-by-step explanation:
Answer:
x : y : z = 9 : 10 : 6
Step-by-step explanation:
Expressing the ratio y : z = 5 : 3 in fractional form, that is
[tex]\frac{y}{z}[/tex] = [tex]\frac{5}{3}[/tex] ( cross- multiply )
5z = 3y ( divide both sides by 5 )
z = [tex]\frac{3}{5}[/tex] y = [tex]\frac{3}{5}[/tex] × 10 = 3 × 2 = 6
Thus
x : y : z = 9 : 10 : 6
Find the slope of the line containing the points (-2,5) and
(-2,0).
Answer:
undefined
Step-by-step explanation:
In the souvenir shop, Gary finds a shirt and a key chain he would like to buy. The shirt costs $13.75 and the key chain costs $2.33. What will be the total of Gary's souvenirs?
Answer:
$16.08
Step-by-step explanation:
13.75+2.33=16.08
Kyle asked a random group of students what their favorite sport was. The results are below. Boys Girls Basketball 10 8 Football 25 7 Soccer 9 19 Baseball 18 22 If Kyle were to randomly select a girl to explain why she likes the sport chosen, what is the probability that he will pick a girl who likes football? A 12.5% B 27.1% C 40.3% D 44.6%
Answer:
The probability that Kyle will pick a girl who likes football is 12.5%.
Step-by-step explanation:
The data provided is as follows:
Boys Girls Total
Basketball 10 8 18
Football 25 7 32
Soccer 9 19 28
Baseball 18 22 40
Total 62 56 118
Compute the probability that Kyle will pick a girl who likes football as follows:
[tex]P(F|G)=\frac{n(G\cap F)}{n(G)}[/tex]
[tex]=\frac{7}{56}\\\\=0.125\\\\=12.5\%[/tex]
Thus, the probability that Kyle will pick a girl who likes football is 12.5%.
What is greater 11/12 or 2 1/3
Answer:
2 1/3
Step-by-step explanation: