Banking — Recurring Deposit Accounts
Introduction
A Recurring Deposit (RD) account is a type of savings account offered by banks where you deposit a fixed amount every month for a fixed period. At maturity, you receive the total deposits plus interest. ICSE Class 10 focuses on computing maturity value using the formula for interest on recurring deposits.
Key Features
- Fixed monthly instalment (say ₹P per month).
- Fixed tenure (n months).
- Interest is compounded quarterly (but ICSE uses a simplified formula).
- Maturity amount = Total deposits + Interest earned.
Interest Calculation Formula (ICSE Method)
In ICSE mathematics, interest on a recurring deposit is calculated using the simple interest formula on each instalment:
Interest (I) = P × n(n + 1) / (2 × 12) × r / 100
Where:
- P = Monthly instalment (in ₹)
- n = Number of months (tenure)
- r = Rate of interest per annum (in %)
Maturity Value (MV)
MV = P × n + I
or
MV = P × n + P × n(n + 1) / (2 × 12) × r / 100
Derivation of the Formula
Each monthly instalment earns simple interest for a different period:
- 1st instalment earns interest for n months.
- 2nd instalment earns interest for (n − 1) months.
- Last instalment earns interest for 1 month.
Total principal for interest calculation = P × [n + (n − 1) + ... + 1] = P × n(n + 1) / 2
Since the rate is per annum, convert months to years:
n(n + 1) / 2 months = n(n + 1) / (2 × 12) years
Interest = Principal × Rate × Time / 100 = P × n(n + 1) / (2 × 12) × r / 100
Worked Examples
Example 1: Basic Maturity Value
Amit deposits ₹2,000 per month in a recurring deposit account for 3 years. The bank pays interest at 8% per annum. Find the maturity value.
Solution:
- P = ₹2,000, n = 3 × 12 = 36 months, r = 8%
Interest = P × n(n + 1) / (2 × 12) × r / 100 = 2000 × 36(37) / (24) × 8 / 100 = 2000 × 1332 / 24 × 0.08 = 2000 × 55.5 × 0.08 = 2000 × 4.44 = ₹8,880
Total deposits = P × n = 2000 × 36 = ₹72,000
Maturity value = 72,000 + 8,880 = ₹80,880
Example 2: Finding the Monthly Instalment
Sanya receives ₹1,02,450 at maturity after depositing monthly for 3 years at 9% p.a. What is her monthly instalment?
Solution:
- Let P be the monthly instalment.
- n = 36 months, r = 9%, MV = ₹1,02,450
I = P × 36 × 37 / (24) × 9 / 100 = P × 1332 / 24 × 0.09 = P × 55.5 × 0.09 = P × 4.995
MV = 36P + 4.995P = 40.995P
Therefore, 40.995P = 1,02,450 P = 1,02,450 / 40.995 P = ₹2,500 (approx.)
Example 3: Finding Rate of Interest
Rohit deposits ₹1,500 per month for 2 years and receives ₹40,500 at maturity. Find the rate of interest.
Solution:
- P = ₹1,500, n = 24 months, MV = ₹40,500
- Total deposits = 1500 × 24 = ₹36,000
- Interest = MV − Pn = 40,500 − 36,000 = ₹4,500
I = P × n(n + 1) / (2 × 12) × r / 100 4500 = 1500 × 24 × 25 / (24) × r / 100 4500 = 1500 × 25 × r / 100 4500 = 37500 × r / 100 4500 = 375r r = 4500 / 375 = 12%
Comparison: RD vs Fixed Deposit
| Feature | Recurring Deposit | Fixed Deposit |
|---|---|---|
| Deposit pattern | Monthly instalments | Lump sum one-time |
| Ideal for | Salaried individuals | Those with surplus funds |
| Interest calculation | Per instalment basis | On full principal |
| Tenure | 6 months to 10 years | 7 days to 10 years |
| Premature withdrawal | Allowed (with penalty) | Allowed (with penalty) |
| Loan facility | Available (up to 90%) | Available (up to 90%) |
Common Mistakes and Fixes
| Mistake | Fix |
|---|---|
| Using n in years instead of months | Convert years to months (× 12) |
| Forgetting to divide by 12 in time conversion | Always use n(n+1)/(2×12) |
| Calculating interest on total sum directly | Use the sum-of-digits method |
| Mistaking MV for deposits only | MV = Deposits + Interest |
ICSE Exam Focus
Recurring deposit problems typically carry 6–10 marks in ICSE examinations. Questions generally require:
- Computing maturity value given P, n, r.
- Finding the monthly instalment given MV and r.
- Finding the rate of interest given MV and P.
- Word problems involving time conversion (years to months).
Marks Blueprint:
| Question Type | Marks |
|---|---|
| Direct maturity value computation | 4 |
| Finding monthly instalment | 4 |
| Finding rate of interest | 4 |
| Word problem / application | 3 |
| Conceptual understanding | 2 |
Self-Test Questions
-
A man deposits ₹600 per month in an RD account for 5 years at 10% p.a. Find the maturity value.
-
Neha receives ₹66,550 at maturity from an RD account. She deposited ₹1,000 per month for 5 years. Find the rate of interest.
-
Ravi wants to accumulate ₹1,00,000 in 3 years through an RD account paying 8% p.a. What should his monthly instalment be?
-
Explain why the interest on an RD is less than the interest on an FD for the same total amount deposited over the same period.
-
A recurring deposit account has a monthly instalment of ₹2,500 for 2 years at 9% p.a. Calculate the interest earned and the maturity value.
Tip: In ICSE exams, always write the formula clearly before substituting values. Partial marks are awarded for correct formula application even if the final arithmetic has a minor error.
