RD Interest: The Sum Formula
Derive and apply I = P * n(n+1)/2 * r/(12*100) for recurring deposits.
Equation
y = 500 * x * (x + 1) / 24 * (3 / 100)
Graph
Table
| x | y |
|---|---|
| 1 | 1.25 |
| 2 | 3.75 |
| 3 | 7.5 |
| 4 | 12.5 |
| 5 | 18.75 |
| 6 | 26.25 |
| 7 | 35 |
| 8 | 45 |
| 9 | 56.25 |
| 10 | 68.75 |
| 11 | 82.5 |
| 12 | 97.5 |
What this lesson covers
What you do
You shape the function y = p * x * (x + 1) / 24 * (r / 100) and watch the graph answer.
Challenges to clear
- Set monthly deposit P = 600 and rate r = 3. The total interest at month 12 (x = 12) is Rs 117.
- Half the months, much less interest: month 6 shows Rs 31.50 — n(n+1) grows fast.
- A larger monthly deposit: slide P to 800.
- Now find the rate that yields Rs 312 of interest by month 12. The n(n+1) term makes the later months carry most of it.
Check yourself
Why does the RD formula use n(n+1)/2?
If the tenure 'n' doubles, what happens to the interest roughly?
- It represents the sum of integers from 1 to n, accounting for interest on each month's deposit. — correct
- It calculates the total amount deposited in the account.
- It is the standard formula for simple interest on a lump sum.
- It adjusts the interest rate for monthly compounding.
- It more than doubles, because both n and the sum of months increase. — correct
- It stays the same, as interest depends only on P and r.
- It halves, because the time per deposit is shorter.
- It doubles exactly, like simple interest on a fixed sum.
Think about it
- I = P · n(n+1)/24 · r/100. With P = 600, n = 12, r = 3: what is I?