What is the formula for the number of periods in future value calculation?

The correct formula for calculating the number of periods in a future value calculation is indeed derived from the standard future value formula, which is FV = PV * (1 + r)^t. In this expression, FV represents the future value, PV is the present value, r is the interest rate per period, and t refers to the number of periods.

To isolate t, we need to rearrange this formula. Starting with the standard future value equation, we first divide both sides by PV, which yields FV/PV = (1 + r)^t. To solve for t, we then take the natural logarithm (ln) of both sides, utilizing the property of logarithms that allows us to bring the exponent down as a coefficient. This results in ln(FV/PV) = t * ln(1 + r). By further isolating t, we divide both sides by ln(1 + r), leading us to the final formula:

t = ln(FV/PV) / ln(1 + r).

This formula allows us to determine how many periods are needed for the present value to grow to the future value at a specified interest rate.

The other options do not accurately represent the calculation of periods in the context of future value