TRAC'S BOOK

Imagine opening a recurring deposit account by saving a fixed monthly sum of \(1000\) rupees for \(12\) months. Each month, you physically add another note into your deposit stack, building up your principal over time. You deposit \(1000\) rupees every month, so at the end of the year, your total deposited principal is \(1000 \cdot 12 = 12000\) rupees.

Part 1

When you leave your money in a bank recurring deposit, the bank calculates interest on the equivalent single month principal sum. By using the sum of consecutive natural numbers, you can easily calculate the interest generated across all monthly installment vectors at an annual rate of \(10\) percent.

Part 2

At the end of the tenure, you collect your full payout from the bank teller. The total cash payout you receive—known as the net maturity value—is the sum of all your original deposits plus the interest accumulated across all deposit vectors.

Part 3

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

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

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.

Part 3

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