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
VladimirAG [237]
3 years ago
8

You find an interest rate of 10% compounded quarterly. Calculate how much more money you would have in your pocket if you had us

ed an account compounded continuously with the same interest rate and principal. Round to the nearest cent and do not include the dollar sign.
NOTE: I only need the formula for this.
Mathematics
1 answer:
Elena-2011 [213]3 years ago
3 0

Answer:

see the explanation

Step-by-step explanation:

we know that    

step 1

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

r=10\%=10/100=0.10\\n=4  

substitute in the formula above

A=P(1+\frac{0.10}{4})^{4t}  

A=P(1.025)^{4t}  

Applying property of exponents

A=P[(1.025)^{4}]^{t}  

A=P(1.1038)^{t}  

step 2

The formula to calculate continuously compounded interest is equal to

A=P(e)^{rt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

r=10\%=10/100=0.10  

substitute in the formula above

A=P(e)^{0.10t}  

Applying property of exponents

A=P[(e)^{0.10}]^{t}  

A=P(1.1052)^{t}  

step 3

Compare the final amount

P(1.1052)^{t} > P(1.1038)^{t}

therefore

Find the difference

P(1.1052)^{t} - P(1.1038)^{t} ----> Additional amount of money you would have in your pocket if you had used a continuously compounded account with the same interest rate and the same principal.

You might be interested in
"If &lt; A and then m&lt; A + m/B = 90°"<br> A. Complement Theorem<br> B. Definition of a Right Angle<br> C. Congruent Complemen
9966 [12]

If < A and then m< A + m/B = 90°, then D. Definition of Complementary Angles

<h3>What is a complementary angle?</h3>

When the sum of two angles is 90°, the angles are said to be complementary. In other words, if two angles add up to form a right angle, they are called complementary angles. The two angles are said to complement each other in this context.

Supplementary angles are two angles that add up to 180 degrees, whereas complementary angles are two angles that add up to 90 degrees.

An angle measuring 72 degrees has a complement of 18 degrees.

Therefore, based on the information given, the correct option is D.

Learn more about complementary angles on:

brainly.com/question/16281260

#SPJ1

8 0
1 year ago
The value of y varies directly with x and y 8 when x 2 find y when x 10 answer
Zielflug [23.3K]
8:2=4:1 Answer y=40
hope this helps.
4 0
3 years ago
Use the graph to answer the questions help!
max2010maxim [7]

Answer:

0; 2; 6; 0 or -1

Step-by-step explanation:

If the question says "f(a)=" they are asking for the y value with the given x such as the two first ones.

If it's "f(x)=a than x=" they are asking you what x is when the (bolded) x is a given value.

5 0
3 years ago
Translate and simplify the expression the sum of fifteen and a number plus twelve
mr Goodwill [35]
I think it might be 15n + 12 sorry if it’s not
3 0
3 years ago
Use the Remainder Theorem to determine which binomial is a factor of the function f(x) = x3 − 2x2 − 19x + 20.
dybincka [34]

Answer:

(x - 1)

Step-by-step explanation:

Given

f(x) = x³ - 2x² - 19x + 20

The sum of the coefficients is 1 - 2 - 19 + 20 = 0

This means that x = 1 is a root and (x - 1) is a factor of f(x)

3 0
3 years ago
Read 2 more answers
Other questions:
  • Morgan uses 1/4 of her supply of raisins to make trail mix and 3/8 of her supply of raisins to make cookies. If morgan uses 5 po
    7·2 answers
  • The diagram shows one way to develop the formula for the area of a circle. Pieces of a circle with radius r are rearranged to cr
    10·2 answers
  • Ashley one 129 pieces of gum playing our county fair at school she gave every student in her math class four pieces she has nine
    10·2 answers
  • In the diagram, what is the measure of angle 1 to the nearest degree?
    10·2 answers
  • (x 4 - 3x 3 + 3x 2 - 3x + 6) (x - 2)
    11·1 answer
  • Which value of y from the set {4, 5, 6, 7} makes this equation true? 2y + 5y = 49
    6·2 answers
  • I NEED HELP AS SOON AS POSSIBLE
    9·2 answers
  • There are 8 squares and 2 circles. What is the simplest ratio of circles to total shapes?
    5·1 answer
  • SOMEONE HELP ME PLEASE
    6·1 answer
  • When factoring the equation 9x2+9x+2 what two numbers will the "9x" term be broken into?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!