What is the total deposit with a fixed monthly interest rate and with more money adding to the deposit each year?

Question

Suppose you have 50 dollars and the fixed monthly interest rate is 5%. After the first year, you add 50 dollars to it for each subsequent years, what is the total amount of money you will get at the end of the three-year period.

I understand in R, it can be simply calculated as

((50 x 1.05^12) +50) x 1.05 ^12) + 50) x 1.05^12 = 540.64

Is there a way I can write a function or loop so when calculating a large number of years, for example, 10 years, 15 years, etc. without typing manually?

Answer 1

You can write a simple loop which might be easy to understand :

get_calc_year_loop <- function(year) {
   ans <- 0
   for(i in seq_len(year)) {
     ans <- (ans + 50)*1.05^12
   }
   return(ans)
}

get_calc_year_loop(3)
#[1] 540.6386

However, you can also do this without loop using Reduce :

get_calc_year <- function(year) {
   Reduce(function(x, y) (x + 50) * 1.05^12, seq_len(year), init = 0)
}
get_calc_year(3)
#[1] 540.6386