Which formula is used to calculate the future value of an investment?

The formula for calculating the future value of an investment is derived from the principle of compound interest. When investing a certain amount of money (the present value), it grows over time at a certain interest rate.

The correct formula indicates that the future value is determined by multiplying the present value by the accumulation factor of (1 + r) raised to the power of n, where r is the interest rate per period and n is the number of periods. This accounts for both the initial investment and the compounded interest earned over time.

For example, if you invest $1,000 at an interest rate of 5% for 3 years, you would use the formula:

Future Value = 1000 × (1 + 0.05)^3 = 1000 × (1.157625) = approximately $1,157.63.

This illustrates how investments grow exponentially due to compound interest, which is reflected in the correct formula. The key to the growth is that interest is earned not only on the initial principal but also on the accumulated interest, resulting in a much higher future value over time compared to simple interest calculations.