Formula for accruing costs

Question

I am trying to work out the formula (pretty sure I leant it at some stage, but I can't for the life of me recall it), for calculating the total cost of, for example, 5 cents accruing every month, for 5 years. Eg, the first month is 5c, the second 10c, the 3rd 15c and so on, for 5 years.

Many thanks in advance.

Answer 1

Hint. One may note that if, for a fixed real number $r$, $$ u_{n+1}=u_n+r,\qquad n=0,1,2\cdots, $$ then

$$ u_n=u_0+n\times r\qquad n=0,1,2\cdots. $$

Then apply it with $r=5$ (cents) and any $u_0$.