Compute values dependent on value in t-1 using tidy

I have a tibble which looks as follows:

df <- tibble(return = c(NA,
                        0.120436251,
                        -0.019871515,
                        0.024876142,
                        -0.013786987,
                        -0.012571415),
             value = c(100,
                       NA,
                       NA,
                       NA,
                       NA,
                       NA))

My goal is to compute the value of all subsequent rows (except the first) using the following formula: (1+return)*lag(value). The expected output should look as follows:

df_1 <- tibble(return = c(NA,
                        0.120436251,
                        -0.019871515,
                        0.024876142,
                        -0.013786987,
                        -0.012571415),
             value = c(100,
                       112.0436,
                       109.8171,
                       112.5490,
                       110.9973,
                       109.6019))

In base R, i can use the following for-loop:

df_1 = df


for (i in 2:nrow(df_1)){
  
  df_1$value[i] <- df_1$value[i-1]*(1+df_1$return[i])
}

The function to use in tidy is probably accumulate, however, when using the following code, for each row I receive a list:

df <- df %>% 
  mutate(Value = accumulate(value, ~if(is.na(.y)) .x*(1+df$return) else .y))

Any help would be appreciated.

Solution

Here are some approaches. (The first two could easily be converted to base R by replacing mutate with transform and using base R pipe.)

library(dplyr)
df %>% mutate(value = c(1, cumprod(1 + return[-1])) * value[1])

library(dplyr)
mult <- function(x, y) x * (1 + y)
df %>% mutate(value = Reduce(mult, init = value[1], return[-1], acc = TRUE))

library(dplyr)
library(purrr)
# mult defined above
df %>% mutate(value = accumulate(return[-1], mult, .init = value[1]))