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.

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)

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 \( t = 4 \)

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

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

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