Banking

ICSE Class 10 · Mathematics · Chapter 2

What this chapter covers

Banks, deposits and interest
The recurring deposit account
Why the instalments earn different amounts of interest
The interest formula
Maturity value
Finding the rate of interest
Finding the monthly instalment
Finding the period
Common mistakes and how to avoid them
Comparing recurring deposit schemes

Key points

A recurring deposit (R.D.) account takes a fixed instalment every month for a fixed number of months and pays back the total deposits with interest at maturity.
The five quantities are the monthly instalment P, the number of months n, the rate r% per annum, the interest I and the maturity value MV.
Each instalment earns interest only for the months it stays in the bank: the first for n months, the last for 1 month.
The equivalent principal for one month is P × (n(n+1))/(2), because 1 + 2 + dots + n = (n(n+1))/(2).
Interest: I = P × (n(n+1))/(2 × 12) × (r)/(100).
Maturity value: MV = P × n + I.
Always convert the period to months before using the formula; r stays per annum.
To find r or P, substitute what is known and solve a linear equation; to find n, solve n(n+1) = value and keep the positive root.
R.D. interest is roughly half the simple interest on the total deposit for the whole period, because the average rupee stays in the bank for about half the time.
Check every answer by putting it back into the formula.

Questions answered

Define a recurring deposit account.

A recurring deposit account is a bank account in which the holder deposits a fixed sum every month for a fixed number of months and receives the total deposits with interest at the end of that period.

Define maturity value and write its formula.

The maturity value is the total amount paid by the bank when the account matures: all the instalments plus the interest. MV = P × n + I.

Why does the first instalment of a recurring deposit earn more interest than the last one?

The first instalment stays in the bank for all n months, while the last stays for only 1 month. Simple interest grows with time, so the earlier money earns more.

Ramesh deposits ₹300 per month for 1 year at 8% per annum. Find the interest and the maturity value.

I = 300 × 6.5 × 0.08 = 156; MV = 3600 + 156 = 3756. Interest ₹156, maturity value ₹3,756.

Find the maturity value of a recurring deposit of ₹1,500 per month for 2 years at 6% per annum.

I = 1500 × 25 × 0.06 = 2250; MV = 36 000 + 2250 = 38 250. The maturity value is ₹38,250.

A recurring deposit of ₹2,000 per month runs for 9 months at 8% per annum. Find the interest and the amount received at maturity.

(9 × 10)/(24) = 3.75; I = 2000 × 3.75 × 0.08 = 600; MV = 18 000 + 600 = 18 600. Interest ₹600, maturity value ₹18,600.

Priya deposits ₹400 per month for 18 months and earns ₹627 as interest. Find the rate of interest.

400 × 14.25 = 5700; 627 = 5700 × (r)/(100), so r = 11. The rate is 11% per annum.

A recurring deposit account for 2 years at 9% per annum pays ₹15,750 at maturity on a monthly instalment of ₹600. Verify the rate by finding it from the other data.

Total deposited = 600 × 24 = 14 400, so I = 1350. 1350 = 600 × 25 × (r)/(100) = 150r, so r = 9. The rate of 9% per annum is confirmed.

Past board exam questions

ICSE 2027 sample paper · 1 mark

Assertion (A): In a recurring deposit account, a man deposits ₹ 1000 per month for 1 year. On maturity he receives ₹ 13500. The amount of interest he earns is ₹1500. Reason (R): Interest earned = Maturity value − Total amount deposited.

(A) is true and (R) is false.
(A) is false and (R) is true.
Both (A) and (R) are true, and (R) is the correct explanation for (A).
Both (A) and (R) are true, but (R) is not the correct explanation for (A).

Show answer

Both (A) and (R) are true, and (R) is the correct explanation for (A).

ICSE 2027 sample paper · 3 marks

A man opened a recurring deposit account in a bank. He deposits ₹ 1000 per month for 2 years. The matured value is equal to 26 times the amount he pays per month. Find the: (a) interest paid by the bank. (b) rate of interest per annum that the bank was paying for the recurring deposit account.

Show answer

P = ₹ 1000, n = 24 months, maturity value = 26 × 1000 = ₹ 26000. (a) Total deposited = 1000 × 24 = ₹ 24000. Interest = ₹ 26000 − ₹ 24000 = ₹ 2000. (b) I = P × (n(n+1))/(2 × 12) × (r)/(100) = 1000 × (24 × 25)/(24) × (r)/(100) = 250r 250r = 2000 ⇒ r = 8% per annum.

ICSE 2026 sample paper · 1 mark

Radha deposited ₹400 per month in a recurring deposit account for 18 months. The qualifying sum of money for the calculation of interest is:

₹ 3,600
₹ 7,200
₹ 68,400
₹ 1,36,800

Show answer

₹ 68,400

ICSE 2026 board paper · 1 mark

A and B opened a recurring deposit account in a bank which is paying simple interest at 9% per annum. A deposited ₹ 1,500 for one year and B deposited ₹ 1,200 for 15 months. The amount invested by:

A is ₹ 27 more than B
A is ₹ 300 more than B
A is ₹ 300 less than B
Both A and B are same (₹ 18,000)

Show answer

Both A and B are same (₹ 18,000)

ICSE 2026 sample paper · 3 marks

Mr. Sam has a recurring deposit account and deposits ₹ 600 per month for 2 years. If he gets ₹ 15,600 at the time of maturity, find the rate of interest earned by him.

Show answer

P = ₹ 600, n = 24 months, let the rate be r%. Interest = 600 × (24 × 25)/(2) × (r)/(100) × (1)/(12) = 150r. Maturity value = 600 × 24 + 150r = 14400 + 150r = 15600. 150r = 1200 ⟹ r = 8%.

ICSE 2026 board paper · 3 marks

Rohit and Vinay both opened a recurring deposit account in a bank for 2 years at 8% simple interest. Vinay deposited ₹ 300 per month. On maturity, Rohit's interest was ₹ 800 more than Vinay's interest. Find the: (a) interest earned by Vinay. (b) sum deposited by Rohit every month.

Show answer

n = 24 months, r = 8%. Interest = P × (n(n+1))/(2 × 12) × (r)/(100) = P × (24 × 25)/(24) × (8)/(100) = 2P. (a) Vinay: P = 300, interest = 300 × 25 × (8)/(100) = ₹ 600. (b) Rohit's interest = ₹ 600 + ₹ 800 = ₹ 1,400. 2P = 1400 ⇒ P = ₹ 700 per month.

ICSE 2025 board paper · 1 mark

Mr. Anuj deposits ₹500 per month for 18 months in a recurring deposit account at a certain rate. If he earns ₹570 as interest at the time of maturity, then his matured amount is:

₹(500 × 18 + 570)
₹(500 × 19 + 570)
₹(500 × 18 × 19 + 570)
₹(500 × 9 × 19 + 570)

Show answer

₹(500 × 18 + 570)

ICSE 2025 sample paper · 1 mark

Radha deposited ₹400 per month in a recurring deposit account for 18 months. The qualifying sum of money for the calculation of interest is:

₹ 3600
₹ 7200
₹ 68,400
₹ 1,36,800

Show answer

₹ 68,400