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
cindy can bake 36 cupcakes in 1 hour. she needs a total of 144 cupcakes. she has already made 18 cupcakes. how many hours will i
aleksklad [387]

Answer:

The answer would be 4 more hours.

Step-by-step explanation:

Since she can make 36 cupcakes in 1 hour,

<u>144 divided by 36 is 4,</u> so it would take four more hours to make the rest.


Hope I helped! God bless you :-)

3 0
3 years ago
You bought 4 notebooks for $0.89 each and some reams of paper at a cost of $1.69 each.
sukhopar [10]

Answer:

5

Step-by-step explanation:

6 0
3 years ago
How many marbles must be in the 8th line ? 
Nat2105 [25]

Answer:

?? Which line

7 0
3 years ago
Read 2 more answers
What type of triangle is this?<br> A. Right<br> B. Equilateral <br> C. Isosceles <br> D. Scalene
balu736 [363]

Answer:

It's an Equilateral triangle

Step-by-step explanation:

This is because of the fact that all of its sides are equal

8 0
3 years ago
Read 2 more answers
(A3- 2a2) - ( 3a2- 4a3)
Tanzania [10]
If you would like to calculate (a^3 - 2 * a^2) - (3 * a^2 - 4 * a^3), you can do this using the following steps:

(a^3 - 2 * a^2) - (3 * a^2 - 4 * a^3) = a^3 - 2 * a^2 - 3 * a^2 + 4 * a^3 = 5 * a^3 - 5 * a^2

The correct result would be 5 * a^3 - 5 * a^2.
8 0
3 years ago
Read 2 more answers
Other questions:
  • Can someone check questions?
    12·1 answer
  • Express 30 minutes per day as a ratio in simplest form.
    8·2 answers
  • Find the inverse of the function y = x^2 + 12x
    12·1 answer
  • Solve the equation. 19 + n = 30 19+n=3019, plus, n, equals, 30 n = n=
    8·1 answer
  • 10r-5r+3r-8r what the answer
    7·1 answer
  • In an over-fished area, the catch of a certain fish is decreasing exponentially.? Use k=0.084 to determine how long will it take
    15·1 answer
  • Allison is selling and buying baseball cards online. She sells each card for 3.25 and buys each card for 5.50. If she sold 4 car
    14·1 answer
  • Simplify the inequality​
    14·2 answers
  • Will give brainlst <br> Have a nice day
    12·1 answer
  • find the numbers at which f is discontinuous and determine whether f is continuous from the right, or from the left, or neither.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!