Questions:
What are the formulas for discrete and continuous compounding?

I have three options to invest my $200,000 savings for the next 8 years. The first option is to invest them at 8% per annum to be compounded continuously. The second option is to deposit this money for a 6% compounded monthly return. The third option is to invest the money at a 7.5% semi annual compounded return. Which option among these three options offers the highest future value?

Reference answers:
# Formulas

Future value of an investment can be found using the following formulas depending on how the compounding takes place.

## Discrete Compounding

For discrete compounding, the following formula is used:

FV = PV (1+r/m)^nm

- FV = future value
- PV = present value (value today)
- r = return
- m = number of compounding periods
- n = number of years

## Continuous Compounding

For continuous compounding, the following formula is used;

FV = PV*e^rt

FV = future value
PV = present value (value today)
r = return 
t = time period in years

# Option 1 (Continuous)

- FV = PV*e^rt
- FV = $200,000 e^0.08*8
- FV = 379296


# Option 2 (Discrete)

- FV = PV (1+r/m)^nm
- FV = $200,000 (1+0.06/12)^(12*8)
- FV = 322828

# Option 3 (Discrete)

- FV = PV (1+r/m)^nm
- FV = $200,000 (1+0.075/2)^(2*8)
- FV = 360446

# Result

Option 1 offers the highest future value for the $200,000 investment.