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

What is the future value after 12 years if you deposit \( \$ 1,000 \) for your child's education and the interest is guaranteed at \( 1.9 \% \) compounded continuously? (Round your answer to the nearest cent.) \( \$ \)

Ask by Wade Powers. in the United States
Feb 26,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The future value after 12 years is approximately \$1,256.09.

Solution

To find the future value after 12 years with continuous compounding, we can use the formula for continuous compounding: \[ FV = PV \times e^{rt} \] Where: - \( FV \) is the future value - \( PV \) is the present value (initial deposit) - \( r \) is the annual interest rate - \( t \) is the time in years Given: - \( PV = \$1,000 \) - \( r = 1.9\% = 0.019 \) - \( t = 12 \) years Substitute the values into the formula: \[ FV = 1000 \times e^{0.019 \times 12} \] Now, we can calculate the future value using the formula for continuous compounding. Calculate the value by following steps: - step0: Calculate: \(1000e^{0.019\times 12}\) - step1: Multiply the numbers: \(1000e^{0.228}\) - step2: Convert the expressions: \(1000e^{\frac{57}{250}}\) - step3: Rewrite the expression: \(1000\sqrt[250]{e^{57}}\) The future value after 12 years with continuous compounding is approximately $1,256.09.

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

The Deep Dive

To find the future value \( FV \) of an investment compounded continuously, you can use the formula: \[ FV = P \times e^{rt} \] where: - \( P \) is the principal amount (initial deposit), - \( r \) is the interest rate (as a decimal), - \( t \) is the time in years, - \( e \) is the base of the natural logarithm (approximately equal to 2.71828). In this case: - \( P = 1000 \) - \( r = 0.019 \) (1.9% as a decimal) - \( t = 12 \) Plugging in the values: \[ FV = 1000 \times e^{0.019 \times 12} \] Calculating \( e^{0.019 \times 12} \): \[ FV = 1000 \times e^{0.228} \] Now, calculating \( e^{0.228} \) gives approximately 1.256. Now, calculate the future value: \[ FV = 1000 \times 1.256 \approx 1256.63 \] So, the future value after 12 years will be approximately: \[ \boxed{1256.63} \]

Related Questions

1.3.2 Make a conjecture with regard to \( r^{n} \) and \( S_{n} \) as \( n \rightarrow \infty \) (2) 1.4 CASE 3: \( r=1 \) 1.4.1 What is the sum of the geometric series \[ S_{n}=a+a r+a r^{2}+\ldots a r^{n-1} \text { if } r=1 ? \] 1.4.2 Make a conjecture with regard to \( r^{n} \) and \( S_{n} \) as \( n \rightarrow \infty \) 1.5 CASE 4: \( r=-1 \) 1.5.1 What is the sum of the geometric series \[ S_{n}=a+a r+a r^{2}+\ldots a r^{n-1} \text { if } r=-1 ? \] 1.5.2 Do the sums above approach some finite particular number as \( n \rightarrow \infty \) i.e. is the sequence divergent or convergent? 1.6 CASE 5: \( -1<r<1 \) REQUIREMENTS: - One A4 papers - Provided grid 1.6.1 Write THREE possible values of \( r \) such that \( -1<r<1 \). 1.6.2 Step 1. Cut the A4 size paper along the longest side into two equal Rectangles and define their areas to be 16 unit \( ^{2} \). 1.6.3 Step 2. Place one half of the rectangle in Step 1 on the desktop and cut the other half along the longest side in to two equal rectangles. 1.6.4 Step 3. Place one half of the rectangle in Step 2 on the desktop and cut the other half along the longest side into two equal rectangles. 1.6.5 Step 4. Continue with the procedures from Step 3 until you find it too difficult to fold and cut the piece of paper you are holding. 1.6.6 Step 5. The first piece of paper you placed on the desktop has an area of \( \frac{1}{2} \) the area of the A4. The second piece of paper has an area of \( \frac{1}{4} \) the area of the A4. Write the areas of the next three pieces of paper. (3) (I) 1.6.7 Explain why these areas form a geometric sequence.
Pre Calculus South Africa Feb 26, 2025
Let \( f(x)=2 x+1, g(x)=-x^{2}+1 \), and \( h(x)=\frac{1}{x+1} \) The function \( t \) is defined as \( t(x)=\left\{\begin{array}{ll}h(x) & \text { if } x \in(2,6] \\ g(x) & \text { if } x \leq 1\end{array}\right. \) The domain of function \( t \) is:
Pre Calculus South Africa Feb 26, 2025
8. Suppose function \( f \) is odd and function \( g \) is even. Is the function \[ \begin{array}{llll}\text { (a) } f g & \text { (b) } f \circ g & \text { (c) } g \circ f & \text { (d) } f-g\end{array} \]
Pre Calculus South Africa Feb 26, 2025
Use binomial theorem to sadre \( (1-x)^{-1 / 3} \)
Pre Calculus Ghana Feb 26, 2025
Starting with the graph of a basic function, graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Find the domain and range of the function. \( f(x)=-(x+1)^{3}-4 \) Use the graphing tool to graph the equation. The domain of \( f(x) \) is \( (-\infty, \infty) \). (Type your answer in interval notation.) The range of \( f(x) \) is \( \square \). (Type your answer in interval notation.)
Pre Calculus United States Feb 26, 2025

Latest Pre Calculus Questions

8. Suppose function \( f \) is odd and function \( g \) is even. Is the function \[ \begin{array}{llll}\text { (a) } f g & \text { (b) } f \circ g & \text { (c) } g \circ f & \text { (d) } f-g\end{array} \]
Pre Calculus South Africa Feb 26, 2025
Use pascaf's triangle to solve \( (1-x)^{-1 / 3} \)
Pre Calculus Ghana Feb 26, 2025
Use binomial theorem to sadre \( (1-x)^{-1 / 3} \)
Pre Calculus Ghana Feb 26, 2025
Solve the equation for \( x \). (Round your answer to three decimal places.) \[ \arctan (2 x-9)=-1 \]
Pre Calculus United States Feb 26, 2025
1.3.2 Make a conjecture with regard to \( r^{n} \) and \( S_{n} \) as \( n \rightarrow \infty \) (2) 1.4 CASE 3: \( r=1 \) 1.4.1 What is the sum of the geometric series \[ S_{n}=a+a r+a r^{2}+\ldots a r^{n-1} \text { if } r=1 ? \] 1.4.2 Make a conjecture with regard to \( r^{n} \) and \( S_{n} \) as \( n \rightarrow \infty \) 1.5 CASE 4: \( r=-1 \) 1.5.1 What is the sum of the geometric series \[ S_{n}=a+a r+a r^{2}+\ldots a r^{n-1} \text { if } r=-1 ? \] 1.5.2 Do the sums above approach some finite particular number as \( n \rightarrow \infty \) i.e. is the sequence divergent or convergent? 1.6 CASE 5: \( -1<r<1 \) REQUIREMENTS: - One A4 papers - Provided grid 1.6.1 Write THREE possible values of \( r \) such that \( -1<r<1 \). 1.6.2 Step 1. Cut the A4 size paper along the longest side into two equal Rectangles and define their areas to be 16 unit \( ^{2} \). 1.6.3 Step 2. Place one half of the rectangle in Step 1 on the desktop and cut the other half along the longest side in to two equal rectangles. 1.6.4 Step 3. Place one half of the rectangle in Step 2 on the desktop and cut the other half along the longest side into two equal rectangles. 1.6.5 Step 4. Continue with the procedures from Step 3 until you find it too difficult to fold and cut the piece of paper you are holding. 1.6.6 Step 5. The first piece of paper you placed on the desktop has an area of \( \frac{1}{2} \) the area of the A4. The second piece of paper has an area of \( \frac{1}{4} \) the area of the A4. Write the areas of the next three pieces of paper. (3) (I) 1.6.7 Explain why these areas form a geometric sequence.
Pre Calculus South Africa Feb 26, 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