Suppose I invest $1000 on 1 Jan each year, and it earns interest at 12% pa, compounded monthly. I start on 1 Jan 2022. How much will I have on 31 Dec 2030?
Let $An be the amount the nth deposit grows to. So, $A1 is invested for all of 2022, 2023, 2024, ... and 2030, so for 9 years:
A_1 =...