# Assume the rate as been negative
# Calculate the future value
initial_investment = 100
growth_rate = -0.05
growth_periods = 10
future_value = initial_investment*(1 + growth_rate)**(growth_periods)
print("Future value: " + str(round(future_value, 2)))

# Calculate the discount factor
discount_factor = 1/(1 + growth_rate)**(growth_periods)
print("Discount factor: " + str(round(discount_factor, 2)))

# Derive the initial value of the investment
initial_investment_again = future_value * discount_factor
print("Initial value: " + str(round(initial_investment_again, 2)))