How should the future value equation be modified if compounding occurs more frequently than annually?

divide the interest rate by the number of compounding periods/year

multiply the timespan by the number of periods/year.

To modify the future value equation when compounding occurs more frequently than annually, we need to consider the effect of compounding periods on the interest calculation. The future value (FV) of an investment can be calculated using the formula:

FV = PV * (1 + r/n)^(n*t)

Where:
FV = Future Value
PV = Present Value
r = Annual interest rate
n = Number of compounding periods per year
t = Number of years

If compounding occurs more frequently than annually, we need to adjust the variables in the formula accordingly. Here's how you can modify the equation:

1. Adjust the interest rate: Divide the annual interest rate (r) by the number of compounding periods per year (n). This gives you the periodic interest rate (i).

i = r/n

2. Adjust the number of compounding periods: Multiply the number of years (t) by the number of compounding periods per year (n). This gives you the total number of compounding periods (m).

m = n*t

3. Plug the adjusted values into the modified future value equation:

FV = PV * (1 + i)^m

So, to calculate the future value when compounding occurs more frequently than annually, divide the annual interest rate by the number of compounding periods per year, adjust the number of compounding periods by multiplying the number of years by the number of periods per year, and use the modified equation: FV = PV * (1 + i)^m.