ICSE Class 10 > Class 10 Notes > Mathematics > Chapter Notes: Banking
Chapter Notes: Banking
Introduction
Imagine a piggy bank that not only keeps your money safe but also makes it grow over time! That's what banking with a recurring deposit account is all about. This chapter takes you into the world of banking, where you learn how banks help people save, lend, and manage money. A recurring deposit account is like a disciplined savings plan, where you deposit a fixed amount every month and watch it grow with interest. Whether it's planning for a future goal or understanding how banks work, this chapter is your guide to mastering the basics of banking and the magic of recurring deposits.
- Banking is the process of accepting, protecting, and lending money.
- People deposit spare money in banks to keep it safe and earn interest.
- Banks lend money to individuals or businesses for starting or expanding ventures.
- Banks charge a higher interest rate on loans than they pay on deposits.
- Banks offer various services beyond deposits and loans, benefiting individuals and society.
Main functions of a bank:
- Accepting deposits from customers.
- Lending money to those in need, often at concessional rates for specific groups like farmers or small business owners.
- Providing services like money transfers, bill payments, lockers for valuables, traveler's cheques, foreign currency, ATM cards, debit cards, and credit cards.
Example: Many salaried individuals receive their salaries through bank accounts, and banks facilitate payments like school fees, utility bills, and government loan installments in cities.
Types of Accounts
- Banks offer various deposit schemes to suit different needs.
- The most common and popular type discussed here is the Recurring Deposit Account.
Example: A Recurring Deposit Account allows customers to save a fixed amount monthly for a chosen period, earning interest on their savings.
Recurring Deposit Account (R.D. Account)
- A depositor selects a fixed monthly deposit amount and a specific period for the account.
- The period can range from 3 months to 10 years.
- At the end of the period (maturity), the depositor receives a lump sum called the maturity value.
- The maturity value includes the total deposited amount plus interest, compounded quarterly.
- The interest rate is set by the Reserve Bank of India and may change periodically.
Example: If someone deposits ₹200 every month for 36 months, they will receive the total deposited amount plus interest at maturity, based on the bank's interest rate.
Computing Maturity Value of a Recurring Deposit Account
Stepwise Explanation:
- Identify the monthly deposit (P), number of months (n), and annual interest rate (r).
- Calculate the interest using the formula provided.
- Compute the total sum deposited by multiplying the monthly deposit by the number of months.
- Add the total sum deposited and the interest to find the maturity value.
Formulas:
- Interest (I) = P × [n(n+1) / (2 × 12)] × (r / 100)
- Total Sum Deposited = P × n
- Maturity Value (M.V.) = (P × n) + I
- Maturity Value (M.V.) = (P × n) + {P × [n(n+1) / (2 × 12)] × (r / 100)}
Example: Kiran deposited ₹200 per month for 36 months at 11% per annum.
- Given: P = ₹200, n = 36 months, r = 11%
- Interest (I) = 200 × [36(36+1) / (2 × 12)] × (11 / 100) = ₹1,221
- Total Sum Deposited = 200 × 36 = ₹7,200
- Maturity Value = 7,200 + 1,221 = ₹8,421
Solved Examples
Example 1: Mohan deposited ₹80 per month for 6 years at 6% per annum. Find the maturity amount.
- Given: P = ₹80, n = 6 × 12 = 72 months, r = 6%
- Interest (I) = 80 × [72 × 73 / (2 × 12)] × (6 / 100) = ₹1,051.20
- Total Sum Deposited = 80 × 72 = ₹5,760
- Maturity Value = 5,760 + 1,051.20 = ₹6,811.20
Example 2: Mr. R.K. Nair gets ₹6,455 after one year at 14% per annum. Find the monthly installment.
Method 1 (Unitary Method):
Method 1 (Unitary Method):
- Assume P = ₹100, n = 12 months, r = 14%
- Interest = 100 × [12 × 13 / (2 × 12)] × (14 / 100) = ₹91
- Total Deposited = 100 × 12 = ₹1,200
- Maturity Value = 1,200 + 91 = ₹1,291
- For M.V. = ₹6,455, Monthly Installment = (100 / 1,291) × 6,455 = ₹500
- Let monthly installment = ₹x
- Interest = x × [12 × 13 / (2 × 12)] × (14 / 100) = 0.91x
- Total Deposited = 12x
- Maturity Value = 12x + 0.91x = 12.91x
- Given M.V. = ₹6,455, so 12.91x = 6,455
- x = 6,455 / 12.91 = ₹500
Example 3: Ahmed deposits ₹2,500 per month for 2 years and gets ₹66,250 at maturity. Find the interest and rate of interest.
(i) Interest:
(i) Interest:
- Total Deposited = 2,500 × 24 = ₹60,000
- Interest = Maturity Value - Total Deposited = 66,250 - 60,000 = ₹6,250
- Given: P = ₹2,500, n = 24, I = ₹6,250
- Using I = P × [n(n+1) / (2 × 12)] × (r / 100)
- 6,250 = 2,500 × [24 × 25 / (2 × 12)] × (r / 100)
- r = (6,250 × 24 × 100) / (2,500 × 24 × 25) = 10%
Example 4: Monica deposited ₹600 per month at 10% per annum and received ₹24,930 at maturity. Find the time in years.
- Let time = n months, P = ₹600, r = 10%
- Interest = 600 × [n(n+1) / (2 × 12)] × (10 / 100) = [5n(n+1) / 2]
- Total Deposited = 600 × n
- Maturity Value = 600n + [5n(n+1) / 2] = 24,930
- Multiply by 2: 1200n + 5n² + 5n = 49,860
- Simplify: 5n² + 1205n - 49,860 = 0
- Divide by 5: n² + 241n - 9,972 = 0
- Solve quadratic: n = [-241 ± √(241² + 4 × 9,972)] / 2
- n = 36 or -277 (discard negative)
- Time = 36 months = 3 years
The document Chapter Notes: Banking is a part of the Class 10 Course Mathematics Class 10 ICSE.
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FAQs on Chapter Notes: Banking
| 1. What is a Recurring Deposit Account (R.D. Account) and how does it work? |  |
Ans. A Recurring Deposit Account (R.D. Account) is a type of savings scheme offered by banks that allows individuals to save a fixed amount of money regularly over a specified period. The account holder deposits a predetermined sum at regular intervals (usually monthly), and at the end of the tenure, the total amount along with interest is paid out. This account is ideal for individuals who want to save systematically and earn interest on their savings.
| 2. How is the maturity value of a Recurring Deposit Account calculated? | |
Ans. The maturity value of a Recurring Deposit Account is calculated using the formula: Maturity Value = (Monthly Deposit x Number of Deposits) + Interest Earned. The interest is computed on the total amount deposited and is typically compounded quarterly. The exact calculation can vary based on the interest rate offered by the bank and the time period of the deposit.
| 3. What are the benefits of opening a Recurring Deposit Account? | |
Ans. The benefits of opening a Recurring Deposit Account include the ability to save systematically, earn a higher interest rate compared to regular savings accounts, and build a substantial corpus over time. It also instills a disciplined savings habit, provides liquidity, and can be a secure investment option for those looking to save for specific financial goals.
| 4. Can I withdraw money from a Recurring Deposit Account before maturity? | |
Ans. Typically, premature withdrawal from a Recurring Deposit Account is allowed, but it may come with penalties or reduced interest rates. Banks may also have specific conditions regarding the minimum period before which withdrawal is permitted. It's advisable to check with the respective bank for their policies on premature withdrawals.
| 5. What documents are required to open a Recurring Deposit Account? | |
Ans. To open a Recurring Deposit Account, individuals generally need to provide identification documents such as a government-issued ID (like Aadhar card or passport), address proof, and a passport-sized photograph. Some banks may also require income proof or additional documentation depending on their policies.
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