You have a choice to invest in one of three different college funds to save up for college. You need to save at least $14,000 for your first year. In which of the three accounts do you choose to invest your money given that you have $10,000 to invest and you would like to accrue as much interest as possible?
Answers
Answer: C) You choose account #2
===================================================
Explanation:
Let's compute the final balance for account 1.
We'll use the compound interest formula
A = P*(1+r/n)^(n*t)
where,
P = principal or amount depositedr = decimal form of the annual interest raten = number of times we compound the interest per yeart = number of yearswhere in this case
P = 10,000r = 0.035 n = 4 t = 10So with all that in mind, we get
A = P*(1+r/n)^(n*t)
A = 10,000*(1+0.035/4)^(4*10)
A = 14,169.0883793113
A = 14,169.09
Account #1 gets us $14,169.09 which is over our goal of $14,000
--------------------------
Let's repeat this idea for account 3. I'll get back to account 2 in the next section.
For account 3, we have these inputs
P = 10,000r = 0.032n = 1t = 10leading to...
A = P*(1+r/n)^(n*t)
A = 10,000*(1+0.032/1)^(1*10)
A = 13,702.4104633564
A = 13,702.41
This isn't larger than 14,000. So we cannot use account 3. The interest rate is too small and needs to be bumped up.
--------------------------
Now let's compute account 2. We'll use the continuously compounded interest formula which is
A = P*e^(rt)
The P, r and t are the same as before. The 'e' is a constant and it's roughly e = 2.718... similar to how pi = 3.14... approximately.
I recommend using the calculator's stored value of 'e' to get as much accuracy as possible.
So,
A = P*e^(rt)
A = 10,000*e^(0.036*10)
A = 14,333.2941456052
A = 14,333.29
This exceeds 14,000 so we can use this account.
Comparing this to account 1's value (14,169.09), we can see that account 2 gets us the most money over the 10 year time period. Not only does account 2 have the higher interest rate, but it also has an infinitely higher compounding frequency as well. These two factors help contribute as to why account 2 beats out account 1.
This is why we should go for account 2.
Related Questions
simplify [tex]x^{2} - x - 12[/tex]
Answers
Answer:
Step-by-step explanation:
x2 - x - 12
x2 - 4x + 3x - 12
x(x - 4) + 3(x - 4)
(x - 4) (x+ 3)
-4 + 3 will make -1 for -1x
-4 x 3 will make -12
Thus, the factored form will be (x-4)(x+3)
Find the sum of square root 5 and 2 square root 16 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.
Answers
Answer:
sqrt(5) + 8
The result is irrational because the sqrt(5) is a non-repeating, non terminating decimal that cannot be written as a fraction.
Brainliest, please!
Step-by-step explanation:
sqrt(5) + 2sqrt(16)
sqrt(5) + 2(4)
sqrt(5) + 8
The sum of square root 5 and 2 square root 16 in simplest form is, √5 + 8 and it is irrational number
What is square root?In mathematics, square roots is a concept in which, if we multiply square roots of any number by itself then it will give us an original number.
if 'a' is square root of 'b' then it will represent as, a = √b.
Given that,
Two numbers
square root 5
2 square root 16
sum of square root 5 and 2 square root 16 in simplest form = ?
Sum = √5 + 2√16
= √5 + 2×4
= √5 + 8
the maximum possible simplest form is √5 + 8
As it is clear that, it is a irrational number
Because, √5 can not be written in P/Q form
Hence, the sum is √5 + 8
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What percent of 500 is 125
Answers
Answer:
25%
Step-by-step explanation:
125 of 500 can be written as: 125 /500
To find a percentage, we need to find an equivalent fraction with the denominator 100. Multiply both numerator & denominator by 100.
125 /500 × 100 /100
= ( 125 × 100/ 500 ) × 1 /100 = 25 /100
Answer:
25%
Step-by-step explanation:
Of means multiply and is means equals
P *500 = 125
Divide each side by 500
P = 125/500
P = .25
Change to percent form
P = 25%
[tex]2 |3 \sqrt{2} - 2 \sqrt{3} | + |3 \sqrt{8} - 8 \sqrt{3} | + 2 \sqrt{12} [/tex]
.......................
Answers
Answer:
hope it helps
Step-by-step explanation:
Answer:
SEE THE IMAGE FOR SOLUTION..
Hello! I really need some help with this (:
Answers
Answer:
y = 3x + 3
Step-by-step explanation:
As x increases, y increases by 3. Therefore, the slope of the function is 3.
Setting x = 0 will give an output of 3. Therefore, the y-intercept is (0, 3).
Overall, the function rule for the given data set is y = 3x + 3.
Will give brainliest to correct answer
Answers
Answer:
30 lamps
Step-by-step explanation:
30*2= 60
30 lamps
1. How can you find the decimal forms of 3/12 and 2/9 .
Answers
Answer:
3/12 as a decimal is 0.25
2/9 as a decimal is 0.2 reapeted
Answer:
Answer written below
Step-by-step explanation:
Divide 3 by 12 and 2 by 9 using long division solve like normal long division if your divisor is bigger than your dividend add a zero on top and add a zero to the dividend.
Decimal form of 3/12:0.25
Decimal form of 2/9:0.22223
Select the correct answer.
Which graph represents this equation?
Y=3/2x to the second -6x
Answers
Answer:
the answer is D
Step-by-step explanation:
First you make the y = 0 then you swap the sides
3/2x^2-6x=0 then you factor the expressions X * (3/2x-6)=0. when the product of factors 0, one of the factors are 0. X=0 finally solve for the other X. 3/2x-6=0 X=0 X=4
What is the sum of the geometric series below?
3+1+1/3+1/9+1/27
Answers
Answer:
The correct answer for your geometric series is 4 13/27 (mixed form) or 121/27.
Step-by-step explanation:
Answer:
Step-by-step explanation:
r =term 1 ÷ term 2 = 1 ÷ 3 = 1/3
a =term 1 = 3
n = 5
[tex]Sum = \frac{a(1-r^{n})}{1-r}[/tex]
[tex]= \frac{3*(1-(\frac{1}{3})^{5}}{1-\frac{1}{3}}\\\\=\frac{3*(1-\frac{1}{243})}{\frac{2}{3}}\\\\=\frac{3*\frac{242}{243}}{\frac{2}{3}}\\\\=3*\frac{242}{243}*\frac{3}{2}\\\\=\frac{121}{27}\\\\=4 \frac{13}{27}[/tex]
For a company picnic, Jacob ordered a box of fresh-baked gingerbread cookies and sugar cookies. The box included a total of 68 cookies, and 75% of them were gingerbread. How many gingerbread cookies did Jacob get?
Answers
Answer:
51 gingerbread cookies
Step-by-step explanation:
Find how many gingerbread cookies he got by finding 75% of 68:
68(0.75)
= 51
So, Jacob got 51 gingerbread cookies.
Help me pls
Find the missing segment in the image below
Answers
Answer:
The answer is 12
Step-by-step explanation:
You see its because.
Answer:
?=12
Step-by-step explanation:
Using the Thalès's theorem:
[tex]\dfrac{6}{6+4}=\dfrac{?}{20} \\\\?*10=6*20\ (cross\ products)\\\\?=\dfrac{6*20}{10} \ dividing\ by\ 10\\\\?=12[/tex]
2. Solve Equation Below Please Help!!
Answers
Answer:
n = 19
Step-by-step explanation:
get the -37 to the other side and solve it
Answer:
3rd answer
Step-by-step explanation:
-37+n=56
n=56+37
n=93
Dylan is driving to a concert and needs to pay for parking. There is an automatic fee
of $5 just to enter the parking lot, and when he leaves the lot, he will have to pay an
additional s2 for every hour he had his car in the lot. How much total money would
Dylan have to pay for parking if he left his car in the lot for 6 hours? How much
would Dylan have to pay if he left his car in the lot for t hours?
Answers
Answer:
17
Step-by-step explanation:
6 x 2 = 12 so 12 + 5 = 17
Dylan would have to pay $17.
For such questions it is best to form an expression.
The parking fee has a fixed cost of $5.
It also has a cost per hour of $2.
This means that if a person spends t hours at the parking lot, they will have to pay $2 per hour for those t hours.
Expression = 2 x t = 2t
Whole expression including the fixed amount is:
5 + 2t
If Dylan parked for 6 hours therefore, he would pay:
= 5 + 2 t
= 5 + 2 x 6
= $17
Dylan would therefore have to pay $17 if he left his car for 6 hours.
Find out more at https://brainly.com/question/21294839.
Christopher walks 5km south then walks on a bearing of 036º until he is due east of his starting point. How far is he from his starting point, to 1 decimal place?
Answers
Christopher's distance from his starting point is 3.6 km
Since Christopher initially walks South 5 km and then walks on a bearing of of 036º until he is due east of his starting point.
His distance South, his distance from his starting point and his distance from his 036º bearing, all form a right-angled triangle.
This right-angled triangle with opposite side to the angle 036º, as his distance from his starting point, x and the adjacent side to the angle 036º, as his distance 5 km south.
Since we have both the opposite and adjacent sides of a right-angled triangle,
From trigonometric ratios,
tanФ = opposite/adjacent
tanФ = x/5 km
Now Ф = 036º
So, tan36º = x/5km
x = 5 km(tan36º)
x = 5 km (0.7265)
x = 3.633 km
x ≅ 3.6 km to 1 decimal place.
So, Christopher's distance from his starting point is 3.6 km.
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How to slove this one?
Answers
Answer:
turning it I think.........
f(x)=-4+7, what is f(2)
Answers
Answer:
3
Step-by-step explanation:
7-4
What is the answer to 1-x=16-4x and how did u get it?
Answers
Answer:
x=5
Step-by-step explanation:
1 - x = 16 - 4x
Rearrange :
-x +4x = 16 - 1
3x = 15
x = 5.
Hence, there is one solution : {5}
Answer:
x=5
Step-by-step explanation:
1-x=16-4x
-1 -1
-x=15-4x
+4x. +4x
3x=15
/3. /3
x=5
2. If Bill has an apple, an orange, a pear, a grapefruit, a banana, and a kiwi at home and he wants to bring three pieces of fruit to school, how many combinations of fruit can he bring?
Answers
Answer:
6 choose 3 = 20
Step-by-step explanation:
[tex]=\frac{n!}{r!\left(n-r\right)!}[/tex]
6 choose 3 = 20
The total combinations of fruit he can bring is 20 if Bill has an apple, an orange, a pear, a grapefruit, a banana, and a kiwi at home and he wants to bring three pieces of fruit to school the answer is 20.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
Bill has an apple, an orange, a pear, a grapefruit, a banana, and a kiwi at home and he wants to bring three pieces of fruit to school
Total number of fruits = 1+1+1+1+1+1
Total number of fruits = 6
n = 6
He wants to bring three pieces of fruit to school,
r = 3
Total combination:
= C(6, 3)
= 6!/(6-3)!3!
= 720/(6)(6)
= 720/36
= 20 combination
Thus, the total combinations of fruit he can bring is 20 if Bill has an apple, an orange, a pear, a grapefruit, a banana, and a kiwi at home and he wants to bring three pieces of fruit to school the answer is 20.
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The temperature on a winter was -23 °F. The temerature rise by 5 °F when the sun came up. When the sun set again, the temperature dropped by. 7°F. Write and evaluate an exspression to find the temperature after the sun set.
Answers
Answer:
-25
Step-by-step explanation:
First, add 5 to -23 since the temperature is getting hotter.
so -23 +5= -18
Second, minus the answer by 7 since the temperature is now falling down after the sunset.
so -18 -7 = -25
or...
this step can be simplified as:
-23 +5 -7 =. -25
One thousandth of the base unit in length :
One millionth of the base unit in mass :
One thousandth of the base unite in time :
Answers
Step-by-step explanation:
[tex]1 \div 100th[/tex]
For the function y = (x – 4)(2x + 3)
the 2 x-intercepts are
Answers
Answer:
x=4 -3/2 =x
Step-by-step explanation:
y = (x – 4)(2x + 3)
To find the x intercepts set y=0 and solve for x
0 = (x – 4)(2x + 3)
Using the zero product property
0= x-4 0= 2x+3
x=4 -3 = 2x
x=4 -3/2 =x
Answer:
We can find the x intercepts by setting this equation equal to 0.
So we have:
0 = (x-4)(2x+3)
So we get:
x-4 = 0, x = 4
2x+3 = 0, x = -3/2
The x intercepts are 4 and -3/2
Hope this helps!
A square garden has area 1764meter find it's length and perimeter
Answers
Answer:
[tex]area \: of \: a \: squre = {a}^{2} \\ {a}^{2} = 176 \\ a = 13.26m \\ perimeter = 4a = 4 \times 13.26 = 53.04m^2 \\ thank \: you[/tex]
Answer:
Length = 42 mPerimeter = 168 mConcept:
Here, we need to know how to find the area and perimeter of the square.
Area (square) = s²
s = side lengthPerimeter (square) = 4s
s = side lengthSolve:
PART I: Find the lengthGiven information
Area = 1764 m²
Given formula
A = s²
Substitute values into the formula
1764 = s²
Square root both sides
√s² = √1764
[tex]\boxed{s=42m}[/tex]
--------------------------------------------------------------------------------------------------------
PART II: Find the perimeterGiven information
s = 42 m
Given formula
P = 4s
Substitute values into the formula
P = 4 (42)
Simplify by multiplication
[tex]\boxed{P=168m}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
At the laundromat, Carol used to pay $1.50 per load, but the company has increased the price per load by 20%. Estimate the amount Carol will pay to was 6 loads of laundry.
Answers
Answer:
$10.80 (about $11)
Brainliest, please!
Step-by-step explanation:
20% = 0.2
+20% = x 1.2
1.5 x 1.2 = 1.8
1.8 x 6 = 10.8
order the equations by the steepness of the slopes of their graphs from greatest fj least.
Answers
-3x-4
2/3x-5
flattest slope: -1/5x+2
Angle Terminology with Equations
Aug 03, 8:18:32 AM
?
ZA and ZB are complementary angles. If m2A = (2x – 10)° and m
B = (x - 2), then find the measure of ZA.
EN O
Answer:
Submit Answer
attempt 1 out of 2
Pls help
Answers
If both are complementary then their sum will be 90°
[tex]\\ \sf\longmapsto m<A+m<B=90[/tex]
[tex]\\ \sf\longmapsto 2x-10+x-2=90[/tex]
[tex]\\ \sf\longmapsto 2x+x-10-2=90[/tex]
[tex]\\ \sf\longmapsto 3x-12=90[/tex]
[tex]\\ \sf\longmapsto 3x=90+12[/tex]
[tex]\\ \sf\longmapsto 3x=102[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{102}{3}[/tex]
[tex]\\ \sf\longmapsto x=34[/tex]
Now
[tex]\\ \sf\longmapsto <A=2x-10=2(34)-10=68-10=58[/tex]
Teacher Thomas did a survey of primary 6 students to find out how the students go to school.the result are down. given that 110 student go to school by train, how many students go to school by bus? THE RESULT
BUS 140*
CAR 67.2*
CYCLE 44.8*
walk 20*
train 88*
Answers
Answer:
(88°/360°) * total number of students= 110
88x=39600
x=450 students
x is the total number of students
(140/360)*450=175 students going by bus
if u like my answer mark as brainliest
Pls pls help me! What is it
Answers
Answer:
H
Step-by-step explanation:
Jackie
[tex] \sqrt{9} + \sqrt{25} = 3 + 5 = 8[/tex]
Jesse
[tex] \sqrt{9 + 25} = \sqrt{34} [/tex]
Taking the difference, we get the answer to be
[tex]8 - \sqrt{34} [/tex]
Find the missing side. Round answer to the nearest tenth.
Answers
Tanθ = opposite / adjacent
[tex] \tan(32) = \frac{x}{25} \\ 0.624 = \frac{x}{25} \\ x = 15.6 \\ x = 16[/tex]
I hope I helped you ^_^
solve 6 X + 1 / 3+1=×-3/6
Answers
Help!!!
Slove for x.
A.11
B.9
C.13
D.14
Answers
Answer:
Step-by-step explanation:
The secants form a proportion where the full length of the secant is the denominator of a fraction where the numerator is the external part of the secant.
7/(x + 7) = 6/(15 + 6) Cross Multiply after combining
7 / (x + 7) = 6/(21)
6 * (x + 7) = 7 * 21 Remove the brackets
6x + 42 = 147 Subtract 42
6x = 147 - 42
6x = 105 Divide by 6
x = 17.5
I think I've done this correctly. If you find an error, please let me know and I'll open it for editing.
