The geometric-series lesson asked you to hold a thought — here is the payoff. Deposit $D$ at the end of every year at rate $i$: the first deposit compounds for $n - 1$ years, the next for $n - 2$, the last not at all. Add them up and it is literally a geometric series with ratio $1 + i$: $\mathit{FV} = D\,\dfrac{(1+i)^{n} - 1}{i}$ — read aloud: F-V equals D, times one-plus-i to the n, minus one, all over i.

Run the same gears in reverse and you get the loan: $M = \dfrac{P\,i}{1 - (1+i)^{-n}}$ — the level payment $M$ that retires a debt $P$ in exactly $n$ payments. Savings build a balance up; payments tear one down; both are geometric series in a suit. One discipline before any button is pressed: mortgage rates arrive yearly and charge monthly — divide by 12 first.