Login
Premium
Home Question Bank Math Calculus
Question
upstudy study bank question image url

Watch the video and then solve the problem given below.
Click here to watch the video.
Use the compound interest formulas and to solve the problem given. Round answers to the nearest cent.
Find the accumulated value of an investment of for 4 years at an interest rate of if the money is a. compounded semiannually, b. compounded quarterly, c.
compounded month; compounded continuously.
a. What is the accumulated value if the money is compounded semiannually?
(Round your answer to the nearest cent.)

Ask by Barnett Christensen. in the United States
Mar 23,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The accumulated value of the investment compounded semiannually is $31,063.49.

Solution

Let
Using the compound interest formula
substitute the values:
We now compute . Step by step multiplication (approximate values):
  1. ,
  2. ,
  3. ,
  4. ,
  5. ,
  6. ,
  7. ,
Multiplying by the principal:
Rounding to the nearest cent, the accumulated value is

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

The Deep Dive

To find the accumulated value when the money is compounded semiannually, we can use the formula .
Here, , (5.5% expressed as a decimal), (compounded semiannually), and years.
Calculating it:
So, the accumulated value if the money is compounded semiannually is approximately .
Now for the extra nuggets of information:
Did you know that the concept of compound interest dates back to ancient Mesopotamia, around 3000 BC? Back then, early forms of loans and interest were recorded on clay tablets! Fast forward to today, and compound interest is your ticket to financial growth — it’s often called the “eighth wonder of the world” because of its power to grow money over time.
If you’re stuck trying to remember the formulas for compounding at different intervals, a handy tip is to write them down where you study or work on financial problems. Creating a reference sheet can be a lifesaver since it reinforces your memory! Plus, practicing with different scenarios will help you avoid common mistakes, like confusing (the number of compounding periods) or incorrectly identifying as a percentage instead of a decimal.

Related Questions

A species of fish was added to a lake. The population size P(t) of this species can be modeled by the following function, where t is the number of years from the time the species was added to the lake. P(t)=8001+5e−0.4t Find the initial population size of the species and the population size after 7 years. Round your answers to the nearest whole number as necessary. Initial population size: Population size after 7 years:
Calculus United States Mar 28, 2025
1 Find the range of values of x for which (a) y=x2+2x−4 is an increasing function, (b) y=3x2+4x−3 is a decreasing function. The equation of a curve is y=19(3x−1)3−3x. (i) Find the gradient of the normal at the point P where the curve intersects the y-axis. (ii) Find the equation of the normal at P in the form px+qy+r=0, where p,q and r are integers. (iii) The normal at P meets the x-axis at the point Q. Find the area of triangle OPQ. (iv) Find the range of values of x for which y=19(3x−1)3−3x is an increasing function of x.
Calculus Singapore Mar 28, 2025
Note: The tickmarks on the horizontal axis are −12π,−8π,−4π,4π,8π,12π, respectively. Determine the period of the wave above. ◻ 8 Correct response: 2*4*Pi (1 Mark) Click on Verify to continue! (b) Assuming the Fourier series of f(t) is given by f(t)=a02+∑n=1∞(ancos⁡nπLt+bnsin⁡nπLt) where L is the half period. Complete the steps below: (i) Determine the Fourier coefficient a0. Enter EXACT value: a0=12π Correct response: 12π (1 Mark) Click on Verify to continue! (ii) Determine the Fourier coefficient an NOTE: - In Symbolic mode the correct syntax is, say −2n∗π∗((−1)2−3). Take note of * sign. - In Text mode the correct syntax is −2/(n∗Pi)∗((−1)∧2−3). an=
Calculus United Kingdom Mar 28, 2025
It is given that y=(x−3)2x+1. Find the value of x when the rate of decrease of y is twice the rate of increase of x.
Calculus Singapore Mar 28, 2025
Study the scenario and complete the question(s) that follow(s): Designing a Unique Aquarium Tank As an engineer designing custom aquarium tanks, you are tasked with creating a uniquely shaped tank to fit a specific space. The tank's profile is defined by the curves y=−x+2 and y=1, and it is rotated around the line y=−1 to form a distinctive, bowl-like structure. To ensure the tank meets volume requirements for water capacity and aquatic life, you must calculate its total volume using integral methods. Source: Mafemba, J. 2024. Using the shell method, calculate the volume generated by rotating the region around the specified line in the scenario above. (8 Marks)
Calculus South Africa Mar 28, 2025

Latest Calculus Questions

2.1f(x)=x2+2x−15 on [0,5];k=9 2.2f(x)=x3−8 on [1,3];k=0 3. Use the Intermediate Value Theorem for contimous fumetions to shou that the equations have at least one real solution on the giveu interval. 3.1x4+x−3=0 on [1,2] 3.2x5−x2+2x=1 on [0,1]
Calculus South Africa Mar 28, 2025
A4 A pebble is dropped into still water and sets off ripples forming a circular wave. The radius of the wave after t seconds is r meters. In the first few seconds, the radius is defined by the function r=3t−0.5t2. (i) Write down an expression for the area covered by the ripples after (ii) What is the rate of change of this area with respect to time? (iii) How fast is this area changing after 2 seconds?
Calculus Singapore Mar 28, 2025
A species of fish was added to a lake. The population size P(t) of this species can be modeled by the following function, where t is the number of years from the time the species was added to the lake. P(t)=8001+5e−0.4t Find the initial population size of the species and the population size after 7 years. Round your answers to the nearest whole number as necessary. Initial population size: Population size after 7 years:
Calculus United States Mar 28, 2025
A graphing calculator is recommended. Graph the polynomial, and determine how many local maxima and minima it has. y=5x3−5x2−3x The polynomial has ---Select--- v^ and -- Select--- v^ Watch It Need Help?
Calculus United States Mar 28, 2025
Study the scenario and complete the question(s) that follow(s): Designing a Unique Aquarium Tank As an engineer designing custom aquarium tanks, you are tasked with creating a uniquely shaped tank to fit a specific space. The tank's profile is defined by the curves y=−x+2 and y=1, and it is rotated around the line y=−1 to form a distinctive, bowl-like structure. To ensure the tank meets volume requirements for water capacity and aquatic life, you must calculate its total volume using integral methods. Source: Mafemba, J. 2024. Using the shell method, calculate the volume generated by rotating the region around the specified line in the scenario above. (8 Marks)
Calculus South Africa Mar 28, 2025
Prev Next
Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy
Pop-up title
Lorem ipsum dolor sit amet, te everti debitis assentior nam, ne illum utroque principes sed. Ridens phaedrum an vix, qui in dolore appareat.