Question

Find the future value of a \(\$ 6500\) investment if the interest rate is \(6.25 \%\) compounded monthly for 3 years.

Short answer

The future value is approximately $7918.62

Step-by-step solution

Convert interest rate to decimal form

The interest rate is given as 6.25%. Convert this percentage to decimal form by dividing by 100. So the decimal equivalent of 6.25% is \( \frac{6.25}{100} = 0.0625 \)

Plug values into the future value formula

Next, plug the known values into the formula \( FV = PV * (1 + r/n)^(nt) \). The present value \( PV \) is $6500. The interest rate \( r \) is 0.0625. Because the interest is compounded monthly, \( n \) is 12. The time period \( t \) is 3 years. Putting these values into the formula gives \( FV = 6500 * (1 + 0.0625 / 12)^(12 * 3) \)

Calculate the future value

Perform the calculations inside the parentheses first, then do the exponent, and finally the multiplication to get the future value. This gives \( FV = 6500 * (1 + 0.005208)^(36) = 6500 * (1.005208)^(36) = 6500 * 1.218249661 = \$7918.62 \)

Final Answer

After 3 years, a $6500 investment at an annual interest rate of 6.25%, compounded monthly, will grow to approximately $7918.62 .