9.3.2.2 Computing net maturity value payouts for recurring deposit interest vectors (AICCGM)
PT1: Visualizing Deposit Timelines
Think of your monthly deposits as a sequence of timeline bars. Your first monthly deposit earns interest for \(12\) full months, while your second deposit earns interest for \(11\) months, down to your last deposit which earns interest for only \(1\) month. This creates an interest vector corresponding to the total equivalent time of \(\frac{12 \cdot 13}{2} = 78\) single-month interest units.
Part 1
PT2: Summing the Interest Vector
You can visualize the cumulative time vector using a triangular ladder arrangement. The total time for which one monthly installment earns interest equals \(\frac{n(n + 1)}{2}\) months. Dividing this by \(12\) converts the period into total equivalent years for simple interest calculation.
Part 2
PT3: Breakdown of Payout Components
Visualize a stacked bar chart representing your total payout. The large bottom section represents your total principal deposited \(P \cdot n\), while the top section represents the interest vector yield \(I\). Combining these two blocks gives your complete maturity value payout.