df <- data.frame(
    Actual_Value = seq(300, 700, 100),
    Time_Spent = rep(500, 5), #Time_Spent
    Cancelled = 0, #Cancelled
    Cumulative_Cancelled = 0, #Cumulative_Cancelled
    Forecasted_Value = 500, #Forecasted_Value
    Cancelled_Rate = seq(.01, .5,  length.out = 5) #Cancelled_Rate
)

for (i in 2:nrow(df)) {
    df$Forecasted_Value[i] = df$Time_Spent[i] -
    df$Forecasted_Value[i-1] * df$Cancelled_Rate[i] -
    df$Cumulative_Cancelled[i-1]

    df$Cumulative_Cancelled[i] = df$Forecasted_Value[i-1] *
    df$Cancelled_Rate[i] + df$Cumulative_Cancelled[i-1]

    df$Cancelled[i] = df$Forecasted_Value[i-1] * df$Cancelled_Rate[i]
}
sum_of_errors=sum(abs(df$Actual_Value-df$Forecasted_Value)) #want to minimize this