Questions: Finding the future value and interest for an investment account with an annual interest rate of 1.46% quarterly. John invests 4200 into the account for 5 years. How much money is in John's account after 5 years? How much interest is earned on John's investment after 5 years?

Solution Steps

To solve this problem, we need to calculate the future value of an investment using the formula for compound interest. The formula is:

\[ FV = P \times \left(1 + \frac{r}{n}\right)^{n \times t} \]

where:

• \( FV \) is the future value of the investment,
• \( P \) is the principal amount (initial investment),
• \( r \) is the annual interest rate (as a decimal),
• \( n \) is the number of times the interest is compounded per year,
• \( t \) is the number of years the money is invested for.

In this case, the interest is compounded quarterly, so \( n = 4 \). The principal \( P \) is \$4200, the annual interest rate \( r \) is 1.46% (or 0.0146 as a decimal), and the investment period \( t \) is 5 years. After calculating the future value, the interest earned can be found by subtracting the principal from the future value.

We are given the following values:

• Principal amount, \( P = 4200 \)
• Annual interest rate, \( r = 0.0146 \)
• Number of times interest is compounded per year, \( n = 4 \) (quarterly)
• Number of years, \( t = 5 \)

The future value \( FV \) of the investment can be calculated using the compound interest formula:

\[ FV = P \times \left(1 + \frac{r}{n}\right)^{n \times t} \]

Substituting the given values:

\[ FV = 4200 \times \left(1 + \frac{0.0146}{4}\right)^{4 \times 5} \]

After performing the calculations, the future value of the investment is:

\[ FV = 4517.47 \]

The interest earned is the difference between the future value and the principal:

\[ \text{Interest Earned} = FV - P = 4517.47 - 4200 = 317.47 \]

Final Answer