Calculate monthly population estimates based on constant growth factor

Question

I'm hoping there is a simple solution to this, but I'm having trouble working it out.

I have population sizes for some cities, like:

df <- data.frame(city = c("A","B","C","D","E","F","G"), start_pop = c(100,200,300,400,500,600,700))

start_pop is the population in January 2019. Assuming that the population increases by 0.022% each month, I would like to calculate monthly population estimates for each city through 2019, 2020 and 2021, saved as Jan19, Feb19 etc., which relies on the input of the previous calculation.

I can do it with mutate, something like:

increase <- 1.00022
df <- data.frame(city = c("A","B","C","D","E","F","G"), start_pop = c(100,200,300,400,500,600,700)) %>% 
  mutate(Feb19 = start_pop * increase) %>% 
  mutate(Mar19 = Feb19 * increase) %>% 
  mutate(Apr19 = Mar19 * increase)
...

But is there a more succinct way of getting the same result, perhaps through a loop or an apply function?

Answer 1

Will this do?

increase <- 0.00022

df %>% mutate(mon = as.Date("2019-01-01")) %>%
  group_by(city) %>%
  complete(mon = seq.Date(from = as.Date("2019-01-01"), to = as.Date("2021-12-01"), by = "month")) %>%
  mutate(start_pop = if_else(is.na(start_pop), increase+1, start_pop),
         start_pop = cumprod(start_pop)) %>%
  pivot_wider(names_from = mon, values_from = start_pop)

# A tibble: 7 x 37
# Groups:   city [7]
  city  `2019-01-01` `2019-02-01` `2019-03-01` `2019-04-01` `2019-05-01` `2019-06-01`
  <chr>        <dbl>        <dbl>        <dbl>        <dbl>        <dbl>        <dbl>
1 A              100         100.         100.         100.         100.         100.
2 B              200         200.         200.         200.         200.         200.
3 C              300         300.         300.         300.         300.         300.
4 D              400         400.         400.         400.         400.         400.
5 E              500         500.         500.         500.         500.         501.
6 F              600         600.         600.         600.         601.         601.
7 G              700         700.         700.         700.         701.         701.
# ... with 30 more variables: `2019-07-01` <dbl>, `2019-08-01` <dbl>, `2019-09-01` <dbl>,
#   `2019-10-01` <dbl>, `2019-11-01` <dbl>, `2019-12-01` <dbl>, `2020-01-01` <dbl>,
#   `2020-02-01` <dbl>, `2020-03-01` <dbl>, `2020-04-01` <dbl>, `2020-05-01` <dbl>,
#   `2020-06-01` <dbl>, `2020-07-01` <dbl>, `2020-08-01` <dbl>, `2020-09-01` <dbl>,
#   `2020-10-01` <dbl>, `2020-11-01` <dbl>, `2020-12-01` <dbl>, `2021-01-01` <dbl>,
#   `2021-02-01` <dbl>, `2021-03-01` <dbl>, `2021-04-01` <dbl>, `2021-05-01` <dbl>,
#   `2021-06-01` <dbl>, `2021-07-01` <dbl>, `2021-08-01` <dbl>, `2021-09-01` <dbl>,
#   `2021-10-01` <dbl>, `2021-11-01` <dbl>, `2021-12-01` <dbl>

Answer 2

Additional solution. Using the approach @AnilGoyal

library(tidyverse)
df <- data.frame(city = c("A","B","C","D","E","F","G"), start_pop = c(100,200,300,400,500,600,700))
n <- 36
increase <- 1.00022
seq_increase <- cumprod(rep(increase, n))
seq_date <- seq.Date(from = as.Date("2019-02-01"), length.out = n, by = "month")

bind_cols(df, 
          map2_dfc(
            .x = seq_increase, 
            .y = seq_date,
            .f = ~transmute(df, !!paste0(.y) := start_pop * .x)))
#>   city start_pop 2019-02-01 2019-03-01 2019-04-01 2019-05-01 2019-06-01
#> 1    A       100    100.022    100.044   100.0660   100.0880   100.1100
#> 2    B       200    200.044    200.088   200.1320   200.1761   200.2201
#> 3    C       300    300.066    300.132   300.1980   300.2641   300.3301
#> 4    D       400    400.088    400.176   400.2641   400.3521   400.4402
#> 5    E       500    500.110    500.220   500.3301   500.4401   500.5502
#> 6    F       600    600.132    600.264   600.3961   600.5282   600.6603
#> 7    G       700    700.154    700.308   700.4621   700.6162   700.7703
#>   2019-07-01 2019-08-01 2019-09-01 2019-10-01 2019-11-01 2019-12-01 2020-01-01
#> 1   100.1321   100.1541   100.1761   100.1982   100.2202   100.2423   100.2643
#> 2   200.2641   200.3082   200.3523   200.3963   200.4404   200.4845   200.5286
#> 3   300.3962   300.4623   300.5284   300.5945   300.6607   300.7268   300.7930
#> 4   400.5283   400.6164   400.7045   400.7927   400.8809   400.9691   401.0573
#> 5   500.6604   500.7705   500.8807   500.9909   501.1011   501.2113   501.3216
#> 6   600.7924   600.9246   601.0568   601.1890   601.3213   601.4536   601.5859
#> 7   700.9245   701.0787   701.2329   701.3872   701.5415   701.6959   701.8502
#>   2020-02-01 2020-03-01 2020-04-01 2020-05-01 2020-06-01 2020-07-01 2020-08-01
#> 1   100.2864   100.3084   100.3305   100.3526   100.3747   100.3967   100.4188
#> 2   200.5728   200.6169   200.6610   200.7052   200.7493   200.7935   200.8377
#> 3   300.8591   300.9253   300.9915   301.0577   301.1240   301.1902   301.2565
#> 4   401.1455   401.2338   401.3220   401.4103   401.4986   401.5870   401.6753
#> 5   501.4319   501.5422   501.6525   501.7629   501.8733   501.9837   502.0941
#> 6   601.7183   601.8506   601.9831   602.1155   602.2480   602.3804   602.5130
#> 7   702.0046   702.1591   702.3136   702.4681   702.6226   702.7772   702.9318
#>   2020-09-01 2020-10-01 2020-11-01 2020-12-01 2021-01-01 2021-02-01 2021-03-01
#> 1   100.4409   100.4630   100.4851   100.5072   100.5293   100.5515   100.5736
#> 2   200.8818   200.9260   200.9702   201.0145   201.0587   201.1029   201.1472
#> 3   301.3228   301.3891   301.4554   301.5217   301.5880   301.6544   301.7207
#> 4   401.7637   401.8521   401.9405   402.0289   402.1174   402.2058   402.2943
#> 5   502.2046   502.3151   502.4256   502.5361   502.6467   502.7573   502.8679
#> 6   602.6455   602.7781   602.9107   603.0434   603.1760   603.3087   603.4415
#> 7   703.0864   703.2411   703.3958   703.5506   703.7054   703.8602   704.0150
#>   2021-04-01 2021-05-01 2021-06-01 2021-07-01 2021-08-01 2021-09-01 2021-10-01
#> 1   100.5957   100.6178   100.6400   100.6621   100.6843   100.7064   100.7286
#> 2   201.1914   201.2357   201.2799   201.3242   201.3685   201.4128   201.4571
#> 3   301.7871   301.8535   301.9199   301.9863   302.0528   302.1192   302.1857
#> 4   402.3828   402.4713   402.5599   402.6484   402.7370   402.8256   402.9142
#> 5   502.9785   503.0892   503.1998   503.3105   503.4213   503.5320   503.6428
#> 6   603.5742   603.7070   603.8398   603.9727   604.1055   604.2384   604.3714
#> 7   704.1699   704.3248   704.4798   704.6348   704.7898   704.9448   705.0999
#>   2021-11-01 2021-12-01 2022-01-01
#> 1   100.7507   100.7729   100.7951
#> 2   201.5014   201.5458   201.5901
#> 3   302.2522   302.3187   302.3852
#> 4   403.0029   403.0915   403.1802
#> 5   503.7536   503.8644   503.9753
#> 6   604.5043   604.6373   604.7703
#> 7   705.2551   705.4102   705.5654

^{Created on 2021-01-31 by the reprex package (v1.0.0)}