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Recurring deposit questions are among the most predictable in ICSE Class 10 maths: one formula, four unknowns. Students still lose marks by putting years where months belong or by forgetting that the maturity value includes the deposits. This post shows where the formula comes from, works through each type of question and lists the slips to avoid.
What does the ICSE syllabus say about recurring deposits?
Under Commercial Mathematics, the ICSE 2027 Mathematics syllabus lists Banking: "Recurring Deposit Accounts: computation of interest and maturity value using the formula"
I = P × n(n + 1) / (2 × 12) × r / 100
MV = P × n + I
Here P is the monthly instalment, n the number of months, r the yearly rate of interest in percent, I the interest and MV the maturity value. In real banking, the RBI's Master Direction on interest rates on deposits classes recurring deposits as a kind of term deposit. The ICSE formula is a simple-interest classroom model, so use it exactly as the syllabus gives it.
Why does the formula have n(n + 1)/2 in it?
Suppose you deposit P at the start of each month for n months. The first instalment stays in the bank for n months, the second for n − 1 months, and the last for one month. Add up the time each rupee spends in the bank:
P × (n + (n − 1) + ... + 2 + 1) = P × n(n + 1) / 2 rupee-months
That is the same as one sum of P × n(n + 1)/2 kept for one month. Simple interest for one month at r% a year is that amount × (1/12) × (r/100), which is exactly the syllabus formula. Once you see this, the 12 in the denominator stops being a mystery: it turns the yearly rate into a monthly one.
Worked example 1: interest and maturity value
Riya deposits ₹800 a month for 3 years at 7.5% a year. Find the interest and maturity value.
n = 36 months, so n(n + 1) / (2 × 12) = 36 × 37 / 24 = 1,332 / 24 = 55.5.
I = 800 × 55.5 × 7.5 / 100 = 44,400 × 0.075 = ₹3,330.
Total deposited = 800 × 36 = ₹28,800.
MV = 28,800 + 3,330 = ₹32,130.
Worked example 2: finding the rate
This is the type in the ICSE 2027 specimen paper: ₹1,000 a month for 2 years, and the maturity value is 26 times the monthly instalment.
MV = 26 × 1,000 = ₹26,000. Deposits = 1,000 × 24 = ₹24,000, so I = ₹2,000.
Formula: 2,000 = 1,000 × (24 × 25) / 24 × r / 100 = 1,000 × 25 × r / 100 = 250r.
r = 2,000 / 250 = 8% a year.
This matches the marking scheme's answer of 8% per annum. The same paper has an assertion-reason item resting on the idea that interest earned = maturity value − total amount deposited.
Worked example 3: finding the instalment
An account runs for 2 years at 6% a year and matures at ₹25,500. Find the monthly instalment.
I = P × (24 × 25) / 24 × 6 / 100 = P × 25 × 0.06 = 1.5P.
MV = 24P + 1.5P = 25.5P.
25.5P = 25,500, so P = ₹1,000.
Worked example 4: finding the number of months
₹500 a month at 10% a year earns ₹1,250 interest. How long was the account?
1,250 = 500 × n(n + 1) / 24 × 10 / 100, which simplifies to 1,250 = (50/24) × n(n + 1).
n(n + 1) = 1,250 × 24 / 50 = 600.
24 × 25 = 600, so n = 24 months, or 2 years.
When you reach n(n + 1) = a number, look for two consecutive whole numbers with that product before you reach for the quadratic formula.
Common mistakes and how to avoid them
Using years for n. Convert first: 18 months is n = 18, and 1.5 years is also n = 18.
Calling the interest the maturity value. MV adds back every instalment: P × n + I.
Dividing by 12 twice, once to make r monthly and again in the formula. The formula already has the 12.
Rounding too early. Keep 55.5 or 25 exact until the last step.
A practice routine for recurring deposits
For one week, do four questions a day, one of each type: find I and MV, find r, find P, find n. Write the formula at the top of each answer before you substitute, since that is where method marks start. Then mix in GST and shares questions; Rohrer and Taylor (2007) found that mixed practice produced much better scores a week later than practising one type at a time. Our ICSE Class 10 maths paper guide shows where commercial maths sits in the paper.
If you keep getting stuck at the same step, Fermi's AI tutor can work out what you already know and build a plan for the session, so you sit down to a clear next step.
Before your next study session, derive the formula once on paper from the "first instalment stays n months" idea, without looking.
