Math pls patulong
You are a bank financier. Your bank pays an annual interest rate of 3% compounded
quarterly. If the initial deposit (or principal), of your client is Php 50 000, find the
balance after 5 years.
You have to show the balance of Php 50 000 after 5 years if the bank pays an interest
rate of 3% compounded annually. Which gives a higher interest between the two?
Explain.
Answers
Using compound interest, it is found that:
With interest compound quarterly, the balance is of Php 5,804.With interest compound annually, the balance is of Php 5,796.Due to the higher balance, the quarterly compound gives the higher interest.Compound interest:\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)
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. t is the time in years for which the money is invested or borrowed.
In this problem:
Rate of 3%, hence \(r = 0.03\).Compounded quarterly, hence \(n = 4\).Initial deposit of 50000, hence \(P = 50000\).Five years, hence \(t = 5\).Then, the balance is:
\(A(5) = P\left(1 + \frac{r}{n}\right)^{nt}\)
\(A(5) = 5000\left(1 + \frac{0.03}{4}\right)^{4(5)}\)
\(A(5) = 5804\)
With interest compound quarterly, the balance is of Php 5,804.
Now, with annual interest, we have that \(n = 1\), and:
\(A(5) = P\left(1 + \frac{r}{n}\right)^{nt}\)
\(A(5) = 5000\left(1 + \frac{0.03}{1}\right)^{1(5)}\)
\(A(5) = 5796\)
With interest compound annually, the balance is of Php 5,796.
Due to the higher balance, the quarterly compound gives the higher interest.
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Related Questions
Please tell me or explain how u got the answer
Answers
Answer:
C
Step-by-step explanation:
like terms are terms that are the same, so in c its 7x and 9x. so when you add them it will be 16x, or you can multiply them or do whatever you want with them
What is 6 more than 5 times a number (x)
Answers
Answer:
1 cause 6times1 is 5 or its 3p cause 6times5 is 30
\( \frac{2}{5} + \frac{2}{6} \)
write your answer as an improper fraction, a mixed number and a decimal.
Answers
Question 4 of 9
A line passes through the point (-2,-8) and has a slope of
2
Write an equation in slope-intercept form for this line.
Question 5 of 9
Answers
Answer:
y+8=2(x+2)
this is the slope intercept form
Mr Saver invests $X at t = 0 in an account that pays a nominal rate of R convertible
quarterly. The interest he earns during t = 0. 5 to t = 1. 5 is 1. 0816 times the interest
he earns during t = 0 to t = 1. Find the exact value of R
Answers
The exact value of R is 0.16 or 16% using compound interest.
To find the exact value of R, we need to use the formula for compound interest. The formula for compound interest is: A = P(1 + r/n)^(nt)Where A is the final amount, P is the principal amount, r is the nominal interest rate, n is the number of times interest is compounded per year, and t is the number of years.
We can plug in the values given in the question to find R. The interest earned during t = 0.5 to t = 1.5 is 1.0816 times the interest earned during t = 0 to t = 1.
So, we can set up an equation:1.0816(P(1 + R/4)^(4*1)) = P(1 + R/4)^(4*1.5)Simplifying the equation gives us:1.0816 = (1 + R/4)^0.5
Taking the square root of both sides gives us:1.04 = 1 + R/4Subtracting 1 from both sides and multiplying by 4 gives us:R = 0.16Therefore, the exact value of R is 0.16 or 16%.
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Tom and David get their haircut at the barber shop on Saturdays Tom gets his haircut every four weeks David gets his haircut every six weeks one Saturday Tom and Dave got their haircut at the same time when will Tom and David get their haircut the same day again
Answers
Step-by-step explanation:
Think of it as a ratio problem.
Tom gets his haircut every 4 weeks and David gets his haircut every 6 weeks. So you can write it as 4:6.
The easiest way that I know of to do this is to find multiples.
4: 4x2=8 4x3=12
6: 6x2=12
So the twelfth week they will get their haircuts the same day.
Marina can bicycle 19. 5 miles in the same time it takes her to run 6 miles. She bikes 9 miles per hour faster than she runs. At what speed does Marina run?.
Answers
Speed is the rate at which a body changes its position. The speed by which Marina runs is 4 miles/ hr.
What is Speed?Speed is the rate at which a body changes its position. It is given by the formula,
\(\rm{Speed = \dfrac{Distance}{Time}\)
Given to us
Marina can bicycle 19. 5 miles at the same time it takes her to run 6 miles.
Marina bikes 9 miles per hour faster than she runs.
Let the speed of the Marina running be s, and the time is taken to run 6 miles be t.
Time is taken by Marina to cover a distance of 6 miles by running,
\(\rm t = \dfrac{6\ miles}{s}\)
Since the speed of Marina's bicycle is 9 miles per hour faster than she runs. Time is taken by Marina to cover a distance of 19. 5 miles by bicycle,
\(\rm t = \dfrac{19.5\ miles}{s+9}\)
We know that Marina can bicycle 19. 5 miles at the same time it takes her to run 6 miles. therefore,
\(\rm t = \dfrac{6\ miles}{s}= \dfrac{19.5\ miles}{s+9}\)
\(\dfrac{6}{s}= \dfrac{19.5}{s+9}\)
Solving the given equation we will get,
\(\rm s = 4\ miles/hr\)
Hence, the speed by which Marina runs is 4 miles/ hr.
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Pat and kim bought the same item. Pat said he paid 20% less than the list price. Kim said that if she paid 25% more for the item she would have paid the list price. Who paid the least?
Answers
She says she needs to pay 25% more to pay list price which mean she only paid 75% of the list price while pat paid 80% of the list price
what is 5672 divided by 67-12*87-1/4
Answers
Answer:
\( - \frac{257171}{268} \)
Step-by-step explanation:
\(5672 \div 67 - 12 \times 87 - \frac{1}{4} \)
\( \frac{5672}{67} - 12 \times 87 - \frac{1}{4} \)
\( \frac{5672}{67} - 1044 - \frac{1}{4} \)
\( \frac{22688 - 279792 - 67}{268} \)
\( \frac{ - 257171}{268} \)
\( = - \frac{257171}{268} \)
Find the value of x in each case. Please put statement reasons.
Answers
Answer:
x = 10°
Step-by-step explanation:
Given the figure with angles 2x, 4x, 5x, and 50° marked, you want to find the value of x.
Development∠HAC = ∠HCA . . . . base angles of isosceles triangle HAC
2(∠HAC) = 4x . . . . . exterior angle 4x is equal to the sum of the equal remote interior angles HAC and HCA
∠HAC = 2x . . . . . . . divide by 2
∠AED = 180° -2x -2x = 180° -4x . . . . sum of angles in ∆AED is 180°
∠AHC = 180° -4x . . . . angles at H are a linear pair
HC ║ ED . . . . converse of corresponding angles theorem
∠FEG = ∠FCH = 50° . . . . . corresponding angles theorem
5x = 50° . . . . . substitute value of ∠FEG
x = 10° . . . . . divide by 5
Using this value for the marked angles, we get the measures shown in the attachment.
Please help me!!
Find the measure of the following angles:
D
X
o
4xº
(x + 18)°
B
А
o
С
There needs to be an answer for
Answers
\({\color{chartreuse}{Measure\:of\: ∠\:on\: one\: side\:of\:line\:=\:180°}}\)
∠ Given are (x + 18)° , x° , 4x° and one Angle is 90° as per diagram
Let ,
1st∠ = (x + 18)°
2nd∠ = x°
3rd∠ = 4x°
so ,
\(⟶\:(x \:+\: 18)°\:+\:x°\:+\: 4x°\:+\:90°\:=\:180°\)
\(⟶\:6x°\:+ \:18°\:+\:90°\:=\:180°\)
\(⟶\:6x°\:+ \:108°\:=\:180°\)
\(⟶\:6x°\:=\:180°\:-\:108°\)
\(⟶\:6x\:=\:72°\)
\(⟶\:x\:=\:\frac{72}{6} \\\)
\(⟶\:x\:=\:12°\)
substituting x = 12 at the place of x .
= x° + 18°
= 12° + 18 °
1st∠ = 30°
__________________________________
= x°
2nd∠ = 12°
__________________________________
= 4x°
= 4(12)°
3rd∠ = 48°
help!
Given f(x)=−2x+5, find
f(−1).
Answers
Firstly we need to add one to both sides
2x=6
Then divide both sides by 2x
2x/2x=6/2x
=3
HELP NOW!!?!! who ever gets all three of them right gets brainlist and (15 points) *questions in photo*
Answers
Answer:
1. 1,518,720
2. B = 458
3. Leah
Step-by-step explanation:
1. In order to get the first answer you must multiply 48 by 56 and then multiply that by the cost per feet to get your answer.
\(48=56\)
\(48\times56=2688\)
\(2688\times565=1518720\)
\(=1518720\)
2. In order to get the answer to this question you need to find the amount of necklaces both girls created and then multiply that number by the number of beads on those necklaces.
\(G=106\)
\(106+39=145\)
\(L=145\)
\(106\times104=210\)
\(145\times104=249\)
\(210+249=459\)
\(=458b\)
3. In order to find the answer to this question you need to calculate how much each the girls made then compare.
\(G=106\)
\(L=145\)
\(106\times14=1484\)
\(14+10=24\)
\(145\times24=3480\)
\(1484 < 3480\)
\(=3480L\)
Hope this helps.
Find the value of p .
A. 15
B. 3
C. 30
D. 28
Answers
Answer:
7p+7=37-3p
10p=30
p=3
answer : p=3 because ke=be
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.030.03 with 9090 % confidence if (a) she uses a previous estimate of 0.580.58 ? (b) she does not use any prior estimates?
Answers
the sample size required to estimate the proportion of adults with high-speed Internet access depends on whether a prior estimate is 753
(a) When using a previous estimate of 0.58, we can calculate the sample size. The formula for sample size estimation is n =\((Z^2 p q) / E^2,\) where Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion, q is 1 - p, and E is the desired margin of error.
Using a Z-score of 1.645 for a 90% confidence level, p = 0.58, and E = 0.03, we can calculate the sample size:
n = \((1.645^2 0.58 (1 - 0.58)) / 0.03^2\)) ≈ 806.36
Therefore, a sample size of approximately 807 should be obtained.
(b) Without any prior estimate, a conservative estimate of 0.5 is commonly used to calculate the sample size. Using the same formula as above with p = 0.5, the sample size is:
n = \((1.645^2 0.5 (1 - 0.5)) / 0.03^2\) ≈ 752.89
In this case, a sample size of approximately 753 should be obtained.
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4. Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
a= 8.1 in
b= 13.3 in
c= 16.2 in
ANSWERS:
1. A = 27.9°, B=54.8°, C=97.3°
2. A = 29.9°, B=54.8°, C=95.3°
3. No triangle satisfies the given conditions
4. A= 31.9°, B=52.8°, C=95.3°
Answers
Answer:
To determine the missing parts of the triangle, we can use the law of cosines, which states that for a triangle with sides of lengths a, b, and c and angles opposite those sides of A, B, and C, respectively:
c^2 = a^2 + b^2 - 2ab cos(C)
b^2 = a^2 + c^2 - 2ac cos(B)
a^2 = b^2 + c^2 - 2bc cos(A)
Using the given values of a, b, and c, we can solve for the angles A, B, and C.
a = 8.1 in
b = 13.3 in
c = 16.2 in
c^2 = a^2 + b^2 - 2ab cos(C)
cos(C) = (a^2 + b^2 - c^2) / (2ab)
cos(C) = (8.1^2 + 13.3^2 - 16.2^2) / (2 * 8.1 * 13.3)
cos(C) = 0.421
C = cos^-1(0.421)
C ≈ 97.3°
b^2 = a^2 + c^2 - 2ac cos(B)
cos(B) = (a^2 + c^2 - b^2) / (2ac)
cos(B) = (8.1^2 + 16.2^2 - 13.3^2) / (2 * 8.1 * 16.2)
cos(B) = 0.268
B = cos^-1(0.268)
B ≈ 54.8°
We can find angle A by using the fact that the sum of the angles in a triangle is 180°:
A = 180° - B - C
A = 180° - 54.8° - 97.3°
A ≈ 27.9°
Therefore, the missing parts of the triangle are:
A ≈ 27.9°
B ≈ 54.8°
C ≈ 97.3°
So, the answer is option 1.
find the volume of a pyramid with a square base, where the area of the base is 4.6 cm 2 4.6 cm 2 and the height of the pyramid is 2.3 cm 2.3 cm. round your answer to the nearest tenth of a cubic centimeter.
Answers
The volume of pyramid is 3.5 cm³.
To find the volume of a pyramid with a square base, where the area of the base is 4.6 cm² and the height of the pyramid is 2.3 cm, we can use the following formula:
V = (1/3)B*h
Where V is the volume of the pyramid, B is the area of the base, and h is the height of the pyramid. Substitute the given values into the formula and solve:
V = (1/3)(4.6)(2.3)V = 3.53 cm³
Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is 3.5 cm³. Therefore, the volume of pyramid is 3.5 cm³.
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There are 20%, percent more goblins than wizards in magic club. There are 120 goblins in magic club.
Answers
Answer:
100
Step-by-step explanation:
y = 4x + 12
What is the x - intercept?
Answers
Answer:
The x-intercept is -3
Step-by-step explanation:
So what you need to do is just graph this like any other equation
Start and (0, 12) and make a point
Then the slope is 4 so go up 4 and right 1 and keep doing that.
Then go the opposite direction so down 4 left 1
After that see where the line hits the x-axis, in this case, its (-3, 0)
So the x intercept is -3 or (-3, 0)
Pls mark brainliest because i didn't waste your time lol
Answer: (-3, 0)
Step-by-step explanation: If you want to find the x- intercept for y = 4x + 12, you’ll have to plug y = 0 into the equation and solve the resultint equation 0 = 4x + 12 for x. [0 = 4 x -3 + 12]. Hence, x = -3, so the x - intercept is (-3, 0).
what is the rate of change?
Answers
Exercice 3 Letf:S→Ban application of a setSin a setB. 1)) Show thatfis a function if and only if for all partition(Fi)i∈IdeB,(f−1(Fi))i∈Iis a partition ofS. 2)) Let supposefis a function . show thatfis bijective if and only if for all partition(Hi)i∈JofS,(f(HI))i∈Jis a partition ofB
Answers
There is a unique x∈Hi such that f(x)=y. Explanation:
If f is a function, then for any partition (Fi)i∈I of B, (f−1(Fi))i∈I is a partition of S. This is because for any x∈S, there is a unique y∈B such that f(x)=y. Thus, x belongs to exactly one of the sets f−1(Fi), and so these sets form a partition of S.Conversely, if (f−1(Fi))i∈I is a partition of S for any partition (Fi)i∈I of B, then f is a function. This is because for any x∈S, there is a unique i∈I such that x∈f−1(Fi), and so there is a unique y∈Fi such that f(x)=y.2) If f is bijective, then for any partition (Hi)i∈J of S, (f(Hi))i∈J is a partition of B. This is because for any y∈B, there is a unique x∈S such that f(x)=y. Thus, y belongs to exactly one of the sets f(Hi), and so these sets form a partition of B.Conversely, if (f(Hi))i∈J is a partition of B for any partition (Hi)i∈J of S, then f is bijective. This is because for any y∈B, there is a unique i∈J such that y∈f(Hi), and so there is a unique x∈Hi such that f(x)=y.Explanation:
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suppose a is a set with m elements and b is a set with n elements. a. how many relations are there from a to b? explain. b. how many functions are there from a to b? explain. c. what fraction of the relations from a to b are functions?
Answers
a)There are \(2^m^n\) possible relation
b)Similarly \(n^m\)
c)\(\frac{n^m}{2^m^n}\)
a)Set A has m elements and set B has n elements
Firstly determine the number of elements A*B by using the multiplication rule
Number of elements\(=A*B=m*n=mn\)
For each element, \(A*B\) we have two option
First element 2 ways
Second element 2 ways
mn element 2 ways
By using the multiplication rule
\(2*2*2......=2^m^n }\)
Then there are \(2^m^n\) possible relation
b)Similarly \(n^m\)
c)\(\frac{n^m}{2^m^n}\)
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Find the distance between -6 and 7 on a number line
Answers
Answer:
13
Step-by-step explanation:
13 because negative 6 is 6 away from zero and 7 is 7 away from zero so you add them together to find the distance :D hope this helps
5x +4 = -6 ???? confused a lil
Answers
Answer:
5x+4=-6
5x=-6-4
5x=-10
x=-10/5
x=-2
Step-by-step explanation:
Answer:
\( \sf \: x = - 2\)
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 5x + 4 = -6
Then the value of x will be,
→ 5x + 4 = -6
→ 5x + 4 - 4 = -6 - 4
→ 5x + 0 = -10
→ 5x = -10
→ 5x ÷ 5 = -10 ÷ 5
→ [ x = -2 ]
Hence, the value of x is -2.
Someone please help me solve this lol
Answers
Answer:
obtuse acute
Step-by-step explanation:
An item is regularly priced at $57. It is now priced at a discount of 55% off the regular price.
Answers
Answer:
the item would cost 25.65
Step-by-step explanation:
Which expression is equivalent to 9x + 4y + 2x - y²?
Answers
Answer:
11x + 4y - y^2
Step-by-step explanation:
You plus the same variables, in this time you got 9x and 2x so it's 11x!
Answer:
11x + 4y - y²
Step-by-step explanation:
9x + 4y + 2x - y²
combine like terms
11x + 4y - y²
Timothy is at an elevation of –17.65 meters below sea level. He descends by 3
meters to observe a coral. What is his new elevation relative to sea level?
Answers
If deacending means going down he would be going lower below sea level. This means that three meters are subtracted making the answer -20.65 meters.
The final volume of the acid
A scientist makes an acid solution by adding drops of acid to 1.2 L of water.
were added to the water?
solution is 1.202 L. Assuming the volume of each drop is 0.05 mL, how many drops
About what percent of the acid solution is acid?
Answers
40 drops of acid were added to water and the percentage of acid in acid solution is 0.166% given that scientist makes an acid solution by adding drops of acid to 1.2 L of water and final volume of the acid solution is 1.202 L, provided the volume of each drop is 0.05 mL. This can be obtained by finding volume of the acid added, then the number of acid drops added and the percentage of acid drops in the solution.
Find the number of acid added and the percentage of acid in the solution:Here in the question it is given that,
A scientist makes an acid solutionAcid solution is made by adding drops of acid to 1.2 L of waterThe final volume of the acid solution is 1.202 LVolume of each drop is 0.05 mLWe have to find the number of drops of acid added to water and percentage of acid in the solution.
From the given conditions we can say that volume of acid added to water will be volume of water subtracted from volume of acid solution,
Volume of acid added = Volume of acid solution - Volume of water
Volume of acid added = 1.202 L - 1.2 L
Volume of acid added = 0.002 L
From the given conditions it is given that the volume of each drop is 0.05 mL. Since volume of a drop is in mL, we should convert the volume of acid added from L to mL.
Volume of acid added = 0.002 L
Volume of acid added = 0.002 × 1000 mL
Volume of acid added = 2mL
To find the number of drops of acid added to water divide volume of acid added by volume of a drop,
Number of drops of acid added = 2mL/0.05mL
Number of drops of acid added = 2 × 100/5
Number of drops of acid added = 40 drops
To find the percentage of acid in the acid solution we will have to divide volume of acid added by the volume of acid solution and multiply with 100,
Percentage of acid in acid solution = (0.002 L/1.202 L)100
Percentage of acid in acid solution = 0.00166 × 100
Percentage of acid in acid solution = 0.166%
Hence 40 drops of acid were added to water and the percentage of acid in acid solution is 0.166% given that scientist makes an acid solution by adding drops of acid to 1.2 L of water and final volume of the acid solution is 1.202 L, provided the volume of each drop is 0.05 mL.
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Which account has the highest effective annual interest rate? Account 1: Interest is compounded quarterly at an annual rate of 4.20%. Account 2: Interest is compounded monthly at an annual rate of 4.15%. Account 3: Interest is compounded semiannually at an annual rate of 4.10% Account 4: Interest is compounded annually at a rate of 4.25%.
Answers
Answer:
Account 1 has the highest effective annual interest rate (0.042666142)
Step-by-step explanation:
Hi, to answer this question we have to apply the Effective Annual Interest Rate formula:
EAIR = [(1+r/n)^n ]-1
Where:
r = nominal interest rate
n = number of periods
If interest is compounded annually, then n = 1; if semi-annually, then n = 2; quarterly, then n = 4; monthly, then n = 12
SO:
Account 1: Interest is compounded quarterly at an annual rate of 4.20%.
EAIR = [(1+r/n)^n ]-1 = [(1+(4.20/100)/4)^4 ]-1 = 0.042666142
Account 2: Interest is compounded monthly at an annual rate of 4.15%.
EAIR = [(1+r/n)^n ]-1 = [(1+(4.15/100)/12)^12 ]-1 =0.042298535
Account 3: Interest is compounded semiannually at an annual rate of 4.10%
EAIR = [(1+r/n)^n ]-1 = [(1+(4.10/100)/2)^2]-1 = 0.04142025
Account 4: Interest is compounded annually at a rate of 4.25%.
EAIR = [(1+r/n)^n ]-1 = [(1+(4.25/100)/1)^1 ]-1 = 0.0425
Since:
0.042666142 (1) < 0.0425 (4) < 0.042298535(2) <0.041420258(3)
Account 1 has the highest effective annual interest rate 0.042666142