1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zloy xaker [14]
2 years ago
14

How much more would $1,000 earn in 5 years in an account compounded continuously than an account compounded quarterly if the int

erest rate on both accounts is $3.7%
Mathematics
2 answers:
erik [133]2 years ago
8 0
\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount}
\\\\
A=Pe^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to& \$1000\\
r=rate\to 3.7\%\to \frac{3.7}{100}\to &0.037\\
t=years\to &5
\end{cases}
\\\\\\
A=1000e^{0.037\cdot 5}\implies A=1000e^{0.185}\implies A\approx 1203.21844\\\\
-------------------------------

\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$1000\\
r=rate\to 3.7\%\to \frac{3.7}{100}\to &0.037\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, thus four}
\end{array}\to &4\\
t=years\to &5
\end{cases}
\\\\\\
A=1000\left(1+\frac{0.037}{4}\right)^{4\cdot 5}\implies A=1000(1.00925)^{20}\\\\\\ A \approx 1202.195676

get the difference of the amounts.
s2008m [1.1K]2 years ago
4 0

Answer: There is a difference of $ 1.0228.

Explanation: Given, initial amount or principal = $ 1000,

Time= 5 years and given compound rate of interest = $3.7%

Now, Since the amount in compound continuously,

A= Pe^{rt} , where, r is the rate of compound interest, P is the principal amount and t is the time.

Here, P=$ 1000, t=5 years and r= $3.7%,

Thus, amount in compound continuously ,  A=1000e^{3.7\times5/100}

⇒A=1000e^{18.5}=1000\times 1.20321844013=1203.21844013

Therefore, interest in this compound continuously rate =1203.21844013-1000=203.21844013

now, Since the amount in compound quarterly,

A=P(1+\frac{r/4}{100} )^{4t}, where, r is the rate of compound interest, P is the principal amount and t is the time.

Thus, amount in compound quarterly, A=1000(1+\frac{3.7/4}{100} )^{4\times5}

⇒A=1000(1+\frac{3.7}{400} )^{20}

⇒A=1000(1+\frac{3.7}{400} )^{20}

⇒A= 1202.19567617

Therefore, interest in this compound quarterly rate=1202.19567617-1000=202.19567617

So, the difference in these interests=203.21844013-202.19567617=1.02276396 ≈1.0228                                                  

You might be interested in
WILL MARK BRAINLIEST!!! :)
Vilka [71]

Answer:

A) y = 1/3x + 4

B) y = 1/2x - 9

Step-by-step explanation:

A) In order to find this, we must first solve the initial equation for y to get the slope.

-x + 3y = 6

3y = x + 6

y = 1/3x + 2

Now we know the slope to be 1/3 since parallel lines have the same slope. So we take this slope and the point and use point-slope form to find the equation.

y - y1 = m(x - x1)

y - 5 = 1/3(x - 3)

y - 5 = 1/3x - 1

y = 1/3x + 4

B) To find this line, we again have to find the slope of the initial equation by solving for y.

2x + y = -4

y = -2x - 4

Now we know our new slope to be 1/2. This is because perpendicular lines have opposite and reciprocal slopes. We can use this and the point to solve in the same way.

y - y1 = m(x - x1)

y - - 8 = 1/2(x - 2)

y + 8 = 1/2x - 1

y = 1/2x - 9

3 0
3 years ago
Show work <br> 3=x+3-5x<br> Please help! Thanks!
alexandr1967 [171]

Answer:x=0

Step-by-step explanation:

subtract 3 from both sides

3=3=x+3-5x-3

simplify

0=x-5x

switch sides

x-5x

add similar elements ; x-5x=-4x

-4x=0

divided both side by -4

-4x/-4 . = . 0/-4

=0

5 0
3 years ago
Read 2 more answers
Plz help
german
I think c. 10100÷ (12 x 4)
7 0
3 years ago
Which is the same as 10-2?<br> A) 0.0001 <br> B) 0.001 <br> C) 0.01 <br> D) 100
IceJOKER [234]
The correct answer is C. This is because
10^-2 = 1/10^2 which is 0.01
3 0
3 years ago
Find the perimeter <br><br> 18<br> 34<br> 36<br> 40
Katyanochek1 [597]
I believe that it is 34
3 0
3 years ago
Other questions:
  • What is bigger 3/4 or 3/8
    14·2 answers
  • Which unit rate is equivalent to 15 miles per gallon?
    13·1 answer
  • What is (t^8)^2 ????​
    12·2 answers
  • Your teacher purchases 24 pastries for a class celebration, at $2 each. What integer expresses the amount he paid?
    9·2 answers
  • Figure this out for 15 points
    6·1 answer
  • Angles T and V are complementary. Angle T has a measure of (2x+10) degrees. Angle V has a measure of 48 degrees. What is the val
    13·1 answer
  • Put the equation 3y-4x=-6 into slope intercept form please!!! EXPLAIN!!!!1!!1!!!!
    15·2 answers
  • MULTIPLE CHOICE SHOW YOUR WORK. A bag contains 3 red, 5 yellow, and 7 purple marbles. What is the probability of drawing a purpl
    11·1 answer
  • Help me Plz :))<br> What are the dimensions of AB?
    14·1 answer
  • Determine the surface area of a rectangular prism if
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!