MathsICSE Class 10 · Banking

Recurring Deposit Interest and Maturity Value: Formula and Solved Questions (ICSE Class 10)

Updated 15 October 2026 · Fact-checked

For a recurring deposit of ₹P a month for n months at r% per annum, the interest is I = P × n(n + 1)/(2 × 12) × r/100, and the maturity value is MV = P × n + I. Here n is in months, r is the yearly rate, and P × n is the total deposited.

Each instalment earns interest for fewer months, so the stays add up to n(n+1)/2 rupee-months, which gives the formula.

Illustration drawn for QuestionBuddy.

Understand Recurring Deposit Interest and Maturity Value

In a recurring deposit (RD) account you deposit the same amount every month for a fixed number of months. At the end (the maturity), the bank pays back everything you deposited plus interest. The CISCE syllabus gives the formula to be used:

$I = P \times \frac{n ( n + 1 )}{2 \times 12} \times \frac{r}{100}, M V = P \times n + I,$

where $P$ is the monthly instalment in rupees, $n$ the number of months, $r %$ the rate of interest per annum, $I$ the interest and $M V$ the maturity value.

Why the formula works. The bank pays simple interest on each instalment for the time it stays in the account. The first instalment stays for $n$ months, the second for $n - 1$ months, and so on down to the last, which stays for 1 month. Adding up,

$P \times n + P \times (n - 1) + \dots + P \times 1 = P \times \frac{n ( n + 1 )}{2}$ rupee-months.

This is the same as keeping $P \times \frac{n ( n + 1 )}{2}$ rupees in the bank for one month, that is for $\frac{1}{12}$ year. Simple interest on it is $P \times \frac{n ( n + 1 )}{2} \times \frac{1}{12} \times \frac{r}{100}$ , which is the formula. The quantity $P \times \frac{n ( n + 1 )}{2}$ is often called the equivalent principal for one month.

**Useful values of $\frac{n ( n + 1 )}{24}$ .** For 1 year ( $n = 12$ ) it is $6.5$ ; for 18 months, $14.25$ ; for 2 years, $25$ ; for 3 years, $55.5$ ; for 4 years, $98$ . Notice that 2 years gives almost four times the 1-year value, not twice: interest grows roughly with the square of the time.

Maturity value. The maturity value is the total amount deposited, $P \times n$ , plus the interest. In 2025 Q1(ii) the examiners reported candidates who applied the simple interest formula instead of $M V = P \times n + I$ , and some who chose the option $₹ (500 \times 18 \times 19 + 570)$ , which multiplies the instalment by $n (n + 1)$ .

RD and lump-sum deposits. Because most RD instalments are in the bank for only part of the time, an RD earns much less interest than putting the whole $P \times n$ in at the start for the full period. For one year, the average instalment is in the bank for $6.5$ months.

Recurring Deposit Interest and Maturity Value: formulas to remember

Interest on a recurring deposit: $I = P \times \frac{n ( n + 1 )}{2 \times 12} \times \frac{r}{100}$; $P$ monthly instalment, $n$ months, $r %$ per annum.
Maturity value: $M V = P \times n + I$; Total deposited plus interest.
Equivalent principal for one month: $P_{eq} = P \times \frac{n ( n + 1 )}{2}$; Then $I = P_{eq} \times \frac{1}{12} \times \frac{r}{100}$ .
Months from years: $n = 12 \times (number of years)$; 1.5 years = 18 months; 3 years = 36 months.
Interest is proportional to P and to r: $I \propto P, I \propto r$; Doubling the instalment or the rate doubles the interest.

How to solve Recurring Deposit Interest and Maturity Value questions

Use this routine for every direct recurring deposit question.

1List $P$ , $n$ and $r$ . Convert the time to months.
2Work out $\frac{n ( n + 1 )}{2 \times 12}$ first; it is a single number (for example 25 for 24 months).
3Interest $I = P \times \frac{n ( n + 1 )}{24} \times \frac{r}{100}$ .
4Total deposited $= P \times n$ .
5Maturity value $= P \times n + I$ .
6Write the answer in rupees and say which quantity it is (interest or maturity value).

Recurring Deposit Interest and Maturity Value in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Interest and maturity value of a small RD

Suppose you save ₹500 of your pocket money every month in a recurring deposit for 2 years, and the bank pays 7% per annum.

How much interest will you earn, and how much will you get at maturity?

Try it first, then show the solutionSolution

$n = 24$ , so $\frac{n ( n + 1 )}{24} = \frac{24 \times 25}{24} = 25$ .
$I = 500 \times 25 \times \frac{7}{100} = 875$ .
$M V = 500 \times 24 + 875 = 12000 + 875 = 12875$ .

Answer: Interest ₹875; you receive ₹12,875.

Memory hook: Deposit, wait, collect: the bank returns every instalment plus the interest.

Saving for a known expense

Imagine your parents open a recurring deposit of ₹5,000 a month for 3 years at 7.5% per annum to save for college fees.

Find the maturity value.

Try it first, then show the solutionSolution

$n = 36$ ; $\frac{36 \times 37}{24} = 55.5$ .
$I = 5000 \times 55.5 \times \frac{7.5}{100} = 20812.50$ .
$M V = 5000 \times 36 + 20812.50 = 180000 + 20812.50 = 200812.50$ .

Answer: ₹2,00,812.50 at maturity (interest ₹20,812.50).

Memory hook: Three years of steady saving: 36 instalments, and interest on all of them.

Tricks to remember Recurring Deposit Interest and Maturity Value

Short memory aids. Say each one aloud once, then use it on a question the same day.

Staircase of instalments
Picture a staircase: the first instalment stays $n$ months, the next $n - 1$ , … the last 1 month. The steps add to $\frac{n ( n + 1 )}{2}$ .
Use it when: Remembering why the formula has $n (n + 1)$ .
Two, twelve and a hundred
Divide by 2 (the staircase), by 12 (months to a year) and by 100 (per cent): $\frac{n ( n + 1 )}{2 \times 12} \times \frac{r}{100}$ .
Use it when: Writing the formula correctly under pressure.
Magic numbers
12 months → 6.5; 24 → 25; 36 → 55.5; 48 → 98.
Use it when: Quick checks of $\frac{n ( n + 1 )}{24}$ .
MV = money in + money earned
Maturity value = $P \times n$ (your money) + $I$ (the bank's interest).
Use it when: Avoiding $P \times n (n + 1)$ or forgetting the deposits.

Recurring Deposit Interest and Maturity Value: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Maturity value of a one-year RD · 1 mark · MCQBoard level

Rina deposits ₹600 per month for 1 year in a recurring deposit account at 6% per annum. The maturity value is:
(a) ₹234
(b) ₹7,200
(c) ₹7,434
(d) ₹7,632

Try it first, then show the solutionSolution

$I = 600 \times \frac{12 \times 13}{24} \times \frac{6}{100} = 600 \times 6.5 \times 0.06 = 234$ .
$M V = 600 \times 12 + 234 = 7434$ .

Answer: (c) ₹7,434

Example 2: Interest and maturity value for 2 years · 3 marks · Short answerBoard level

A man deposits ₹1,500 per month in a recurring deposit account for 2 years at 7% per annum. Find the interest and the maturity value.

Try it first, then show the solutionSolution

$n = 24$ , $\frac{n ( n + 1 )}{2 \times 12} = \frac{24 \times 25}{24} = 25$ .
$I = 1500 \times 25 \times \frac{7}{100} = 2625$ .
$M V = 1500 \times 24 + 2625 = 36000 + 2625 = 38625$ .

Answer: Interest ₹2,625; maturity value ₹38,625.

Example 3: Using the equivalent principal · 3 marks · Short answerHarder board level

Asif deposits ₹800 per month for 3 years in a recurring deposit at 9% per annum. (a) Find the equivalent principal for one month. (b) Hence find the interest and the maturity value.

Try it first, then show the solutionSolution

(a) $n = 36$ ; equivalent principal $= 800 \times \frac{36 \times 37}{2} = 800 \times 666 = 532800$ .
(b) $I = 532800 \times \frac{1}{12} \times \frac{9}{100} = 3996$ .
$M V = 800 \times 36 + 3996 = 28800 + 3996 = 32796$ .

Answer: (a) ₹5,32,800 (b) Interest ₹3,996; maturity value ₹32,796.

Example 4: Comparing two deposits with the same total · 4 marks · Short answerHarder board level

Kavya deposits ₹1,000 a month for 2 years at 6% per annum. Rohan deposits ₹2,000 a month for 1 year at 7% per annum. Both deposit ₹24,000 in total. Who gets the larger maturity value, and by how much?

Try it first, then show the solutionSolution

Kavya: $I = 1000 \times 25 \times \frac{6}{100} = 1500$ ; $M V = 24000 + 1500 = 25500$ .
Rohan: $I = 2000 \times 6.5 \times \frac{7}{100} = 910$ ; $M V = 24000 + 910 = 24910$ .
Difference $= 25500 - 24910 = 590$ .
Kavya's money stays in the bank longer on average, so she earns more despite the lower rate.

Answer: Kavya, by ₹590 (₹25,500 against ₹24,910).

Example 5: Why a third year matters so much · 4 marks · Short answerHOTS / competency

A woman deposits ₹1,200 a month in a recurring deposit at 10% per annum. How much more interest would she earn by keeping it for 3 years instead of 2 years? Is the extra interest half of the 2-year interest?

Try it first, then show the solutionSolution

2 years: $I_{2} = 1200 \times 25 \times \frac{10}{100} = 3000$ .
3 years: $I_{3} = 1200 \times 55.5 \times \frac{10}{100} = 6660$ .
Extra interest $= 6660 - 3000 = 3660$ .
Half of ₹3,000 is ₹1,500; the extra ₹3,660 is more than the whole 2-year interest, because $\frac{n ( n + 1 )}{24}$ grows from 25 to 55.5 while $n$ grows only from 24 to 36.

Answer: ₹3,660 more. No: the extra ₹3,660 is more than the whole 2-year interest of ₹3,000, let alone half of it, because RD interest grows roughly with the square of the time.

Example 6: Case study: will the savings be enough? · 4 marks · Case-basedHOTS / competency

Riya opens a recurring deposit of ₹2,500 a month for 15 months at 8% per annum, hoping to have ₹40,000 at maturity to buy a laptop.
(a) Find the interest.
(b) Find the maturity value.
(c) Will she have enough? If not, by how much is she short?

Try it first, then show the solutionSolution

$n = 15$ ; $\frac{15 \times 16}{24} = 10$ .
(a) $I = 2500 \times 10 \times \frac{8}{100} = 2000$ .
(b) $M V = 2500 \times 15 + 2000 = 37500 + 2000 = 39500$ .
(c) $40000 - 39500 = 500$ , so she is ₹500 short.

Answer: (a) ₹2,000 (b) ₹39,500 (c) No, she is ₹500 short.

Where students lose marks in Recurring Deposit Interest and Maturity Value

The slips examiners see most often, and what to write instead.

Mistake: Using years for n
The formula counts instalments, which are monthly.
Wrong working
2 years: $\frac{2 \times 3}{24} = 0.25$ .
Right working
$n = 24$ : $\frac{24 \times 25}{24} = 25$ .
Do this: Write ' $n$ = … months' as your first line.
Usually costs: All the marks; the examiners named this for 2025 Q2(ii), where 3 years was taken as 3 instead of 36.
Mistake: Writing MV with n(n + 1) in place of n, or forgetting the deposits
MV is your total deposits plus interest: $P \times n + I$ . The $n (n + 1)$ belongs only inside the interest formula.
Wrong working
$M V = 500 \times 18 \times 19 + 570$ .
Right working
$M V = 500 \times 18 + 570$ .
Do this: Say aloud: 'money in plus money earned'.
Usually costs: The MCQ in 2025 Q1(ii).
Mistake: Using the simple interest formula on the total deposited
Each instalment is in the bank for a different time.
Wrong working
$I = 24000 \times 2 \times \frac{7}{100} = 3360$ .
Right working
$I = 1000 \times 25 \times \frac{7}{100} = 1750$ .
Do this: Use the RD formula given in the syllabus.
Usually costs: Every mark of the question.
Mistake: Confusing interest with maturity value
The question may give one and ask for the other.
Wrong working
'He gets ₹1,040 as interest' used as the maturity value.
Right working
₹1,040 is $I$ ; $M V = P \times n + 1040$ .
Do this: Underline 'interest' or 'maturity value' in the question.
Usually costs: The examiners named this for 2024 Q4(i).

Exam tips

Write the formula in full, then substitute; the formula line is worth a method mark.
Calculate $\frac{n ( n + 1 )}{24}$ separately and check it against the magic numbers (6.5, 25, 55.5, 98).
In 2025 Q2(ii) the examiners reported candidates who took the time as 3 instead of 36 months and who used the maturity value as the principal.
Give the final answer to the paisa if it is not a whole number of rupees.
If a question asks for 'the amount received', it means the maturity value.

Practice questions on Recurring Deposit Interest and Maturity Value

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
In the formula $I = P \times \frac{n ( n + 1 )}{2 \times 12} \times \frac{r}{100}$ for a recurring deposit, n is:
(a) the number of years
(b) the number of months
(c) the number of instalments minus one
(d) the rate per month
Hint
The 12 in the formula converts months to years.
Answer
(b) the number of months.
Q2 · 3 marks · Short answerBoard level
Find the interest and maturity value of a recurring deposit of ₹400 per month for 1½ years at 8% per annum.
Hint
n = 18, and $\frac{18 \times 19}{24} = 14.25$ .
Answer
$I = 400 \times 14.25 \times 0.08 = ₹456$ ; $M V = 7200 + 456 = ₹7, 656$ .
Q3 · 3 marks · Short answerHarder board level
A teacher deposits ₹3,000 per month for 4 years in a recurring deposit at 6.5% per annum. Find the maturity value.
Hint
$\frac{48 \times 49}{24} = 98$ .
Answer
$I = 3000 \times 98 \times \frac{6.5}{100} = ₹19, 110$ ; $M V = 1, 44, 000 + 19, 110 = ₹1, 63, 110$ .
Q4 · 1 mark · Assertion-reasonHarder board level
Assertion (A): For the same time and rate, doubling the monthly instalment of a recurring deposit doubles the interest.
Reason (R): In the recurring deposit formula the interest is directly proportional to the monthly instalment P.
(a) (A) is true and (R) is false.
(b) (A) is false and (R) is true.
(c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
(d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).
Hint
Look at where P appears in the formula.
Answer
(c)
Q5 · 3 marks · Short answerHarder board level
A recurring deposit of ₹1,000 per month for 2 years earns interest at 7% per annum. If the rate were 8% instead, how much more interest would it earn?
Hint
Only $r$ changes; the extra interest is the interest at 1%.
Answer
$1000 \times 25 \times \frac{1}{100} = ₹250$ more (₹2,000 instead of ₹1,750).
Q6 · 4 marks · Short answerHarder board level
Kunal deposits ₹1,000 every month for 1 year in a recurring deposit at 8% per annum. Meena deposits ₹12,000 at once in a fixed deposit for 1 year at 8% per annum simple interest. (a) Find each one's interest. (b) Explain why Meena earns more although both deposit ₹12,000.
Hint
Think about how long each rupee stays in the bank.
Answer
(a) Kunal: $1000 \times 6.5 \times 0.08 = ₹520$ . Meena: $12000 \times 0.08 = ₹960$ . (b) Meena's whole ₹12,000 earns interest for 12 months; Kunal's instalments stay in the bank for 12, 11, …, 1 months, an average of 6.5 months.
Q7 · 4 marks · Short answerHOTS / competency
Arun wants to earn at least ₹2,000 as interest from a 2-year recurring deposit at 8% per annum. Find the least monthly instalment, and his maturity value with that instalment.
Hint
$I = P \times 25 \times 0.08 = 2 P$ .
Answer
$2 P \geq 2000 \Rightarrow P \geq 1000$ , so ₹1,000 a month. $M V = 24000 + 2000 = ₹26, 000$ .

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Write the interest formula for a recurring deposit.Show answer
$I = P \times \frac{n ( n + 1 )}{2 \times 12} \times \frac{r}{100}$ .
2.What is $\frac{n ( n + 1 )}{24}$ for n = 12?Show answer
6.5
3.₹200 a month for 1 year at 10%: interest?Show answer
$200 \times 6.5 \times 0.1 = ₹130$ .
4.Interest ₹130 on ₹200 a month for 12 months. Maturity value?Show answer
$2400 + 130 = ₹2, 530$ .
5.How long is the first instalment in the bank for an n-month RD? The last?Show answer
n months; 1 month.
6.₹1,000 a month for 2 years at 6%: interest?Show answer
$1000 \times 25 \times 0.06 = ₹1, 500$ .

Recurring Deposit Interest and Maturity Value: frequently asked questions

What is the formula for interest on a recurring deposit in ICSE Class 10?

I = P × n(n + 1)/(2 × 12) × r/100, where P is the monthly deposit, n the number of months and r the rate per cent per annum. The maturity value is P × n + I.

Is n in years or months in the RD formula?

Months. The 12 in the denominator converts the months into years so that the yearly rate can be used.

Why does a recurring deposit earn less interest than a fixed deposit of the same total?

In a recurring deposit only the first instalment stays for the full period; later instalments stay for less time. In a fixed deposit the whole amount earns interest for the whole period.

Is the recurring deposit formula given in the exam?

The formula is written in the CISCE syllabus, but you should know it by heart and write it in your answer before substituting values.