Questions: What is the future value at the end of 4 years of 3,468 invested at an annual interest rate of 5.2% compounded monthly? Answers should be in dollars and correct to 0.01. Give numerical answer only without dollar sign.

What is the future value at the end of 4 years of 3,468 invested at an annual interest rate of 5.2% compounded monthly? Answers should be in dollars and correct to 0.01. Give numerical answer only without dollar sign.
Transcript text: 7 1 point What is the future value at the end of 4 years of $\$ 3,468$ invested at an annual interest rate of $5.2 \%$ compounded monthly? Answers should be in dollars and correct to $\$ 0.01$. Give numerical answer only without dollar sign. Type your answer...
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Solution

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Solution Steps

To find the future value of an investment compounded monthly, we can use the formula for compound interest: \[ FV = P \left(1 + \frac{r}{n}\right)^{nt} \] where:

  • \( FV \) is the future value
  • \( P \) is the principal amount (\$3,468)
  • \( r \) is the annual interest rate (5.2% or 0.052)
  • \( n \) is the number of times interest is compounded per year (12 for monthly)
  • \( t \) is the number of years the money is invested (4 years)
Step 1: Identify the given values

We are given:

  • Principal amount \( P = 3468 \)
  • Annual interest rate \( r = 0.052 \)
  • Number of times interest is compounded per year \( n = 12 \)
  • Number of years the money is invested \( t = 4 \)
Step 2: Apply the compound interest formula

The formula for the future value \( FV \) of an investment compounded monthly is: \[ FV = P \left(1 + \frac{r}{n}\right)^{nt} \]

Step 3: Substitute the given values into the formula

Substituting the given values into the formula, we get: \[ FV = 3468 \left(1 + \frac{0.052}{12}\right)^{12 \times 4} \]

Step 4: Calculate the future value

Performing the calculations: \[ FV = 3468 \left(1 + \frac{0.052}{12}\right)^{48} \] \[ FV = 3468 \left(1 + 0.0043333\right)^{48} \] \[ FV = 3468 \left(1.0043333\right)^{48} \] \[ FV \approx 3468 \times 1.2307 \] \[ FV \approx 4267.93 \]

Final Answer

The future value at the end of 4 years is \( \boxed{4267.93} \).

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