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Class 10 Exam  >  Class 10 Notes  >  Mathematics Class 10 ICSE  >  Worksheet Solutions: Banking

Worksheet Solutions: Banking | Mathematics Class 10 ICSE PDF Download

A. Very Short Answer Questions

Q1. A person deposits ₹300 per month in an RD account for 12 months at 10% p.a. Find the total sum deposited.

Solution — stepwise

  1. Monthly deposit P = ₹300, number of months n = 12.

  2. Total sum deposited = P × n = 300 × 12 = ₹3,600.

Q2. Find the interest earned on ₹100 deposited every month for 12 months at 12% p.a.

Solution — stepwise

  1. P = ₹100, n = 12, r = 12%.

  2. Compute factor n(n+1) / (2 × 12) = 12 × 13 / 24 = 156 / 24 = 6.5.

  3. Interest I = P × factor × (r / 100) = 100 × 6.5 × 12/100 = 100 × 6.5 × 0.12 = 100 × 0.78 = ₹78.

Q3. A person deposits ₹200 per month for 6 months in an RD account at 6% p.a. Find maturity value.

Solution — stepwise

  1. P = ₹200, n = 6, r = 6%.

  2. Total deposited = 200 × 6 = ₹1,200.

  3. Factor = n(n+1) / (2 × 12) = 6 × 7 / 24 = 42 / 24 = 1.75.

  4. Interest I = 200 × 1.75 × 6/100 = 200 × 1.75 × 0.06 = 200 × 0.105 = ₹21.

  5. Maturity value = total deposited + I = 1,200 + 21 = ₹1,221.

Q4. If a person deposits ₹500 monthly for 24 months, what is the total amount deposited?

Solution — stepwise

  1. P = ₹500, n = 24.

  2. Total deposited = 500 × 24 = ₹12,000.

Q5. Find maturity value when P = ₹50, n = 12 months, r = 12% p.a.

Solution — stepwise

  1. Total deposited = 50 × 12 = ₹600.

  2. Factor = 12 × 13 / 24 = 6.5.

  3. Interest I = 50 × 6.5 × 12/100 = 50 × 6.5 × 0.12 = 50 × 0.78 = ₹39.

  4. Maturity value = 600 + 39 = ₹639.

B. Short Answer Type Questions

Q6. Find the maturity value of an RD account in which ₹250 is deposited monthly for 36 months at 8% p.a.

Solution — stepwise

  1. P = ₹250, n = 36, r = 8%.

  2. Total deposited = 250 × 36 = ₹9,000.

  3. Factor = n(n+1)/(2 × 12) = 36 × 37 / 24 = 1332 / 24 = 55.5.

  4. Interest I = 250 × 55.5 × 8/100 = 250 × 55.5 × 0.08 = 250 × 4.44 = ₹1,110.

  5. Maturity value = 9,000 + 1,110 = ₹10,110.

Q7. A student deposits ₹150 per month for 2 years in an RD account at 10% p.a. Find interest and maturity value.

Solution — stepwise

  1. P = ₹150, n = 24, r = 10%.

  2. Total deposited = 150 × 24 = ₹3,600.

  3. Factor = 24 × 25 / 24 = 25.

  4. Interest I = 150 × 25 × 10/100 = 150 × 25 × 0.10 = 150 × 2.5 = ₹375.

  5. Maturity value = 3,600 + 375 = ₹3,975.

Q8. A man deposited ₹500 per month in an RD account for 3 years at 9% p.a. Find the maturity value.

Solution — stepwise

  1. P = ₹500, n = 36 (3 years), r = 9%.

  2. Total deposited = 500 × 36 = ₹18,000.

  3. Factor = 36 × 37 / 24 = 1332 / 24 = 55.5.

  4. Interest I = 500 × 55.5 × 9/100 = 500 × 55.5 × 0.09 = 500 × 4.995 = ₹2,497.50.

  5. Maturity value = 18,000 + 2,497.50 = ₹20,497.50.

Q9. Sita deposited ₹200 per month for 30 months in an RD account at 12% p.a. Find interest earned.

Solution — stepwise

  1. P = ₹200, n = 30, r = 12%.

  2. Total deposited = 200 × 30 = ₹6,000 (for reference).

  3. Factor = 30 × 31 / 24 = 930 / 24 = 38.75.

  4. Interest I = 200 × 38.75 × 12/100 = 200 × 38.75 × 0.12 = 200 × 4.65 = ₹930.

Q10. The maturity value of an RD account is ₹8,421 when ₹200 is deposited every month for 36 months. Find the interest earned.

Solution — stepwise

  1. P = ₹200, n = 36. Total deposited = 200 × 36 = ₹7,200.

  2. Given Maturity value = ₹8,421.

  3. Interest = M.V. − Total deposited = 8,421 − 7,200 = ₹1,221.

C. Long Answer Type Questions 

Q11. Ramesh deposits ₹400 every month for 5 years in an RD account at 9% p.a. Find maturity value.

Solution — stepwise

  1. P = ₹400, time = 5 years ⇒ n = 5 × 12 = 60 months, r = 9%.

  2. Total deposited = 400 × 60 = ₹24,000.

  3. Factor = n(n+1)/(2 × 12) = 60 × 61 / 24 = 3660 / 24 = 152.5.

  4. Interest I = 400 × 152.5 × 9/100 = 400 × 152.5 × 0.09 = 400 × 13.725 = ₹5,490.

  5. Maturity value = 24,000 + 5,490 = ₹29,490.

Q12. A man deposited ₹1,000 per month for 3 years in an RD account and received ₹40,410 at maturity. Find the interest earned and the rate of interest (to two decimal places).

Solution — stepwise

  1. P = ₹1,000, n = 3 years = 36 months. Total deposited = 1,000 × 36 = ₹36,000.

  2. Given M.V. = ₹40,410 ⇒ Interest I = 40,410 − 36,000 = ₹4,410.

  3. Factor for n = 36 is 36 × 37 / 24 = 1332 / 24 = 55.5.

  4. Use I = P × factor × (r / 100). So 4,410 = 1,000 × 55.5 × r / 100 = 55,500 × r / 100 = 555 × r.

  5. Therefore r = 4,410 / 555 = 7.945945...% ≈ 7.95% per annum (rounded to two decimals).

Q13. The maturity value of an RD account is ₹24,930 when ₹600 is deposited monthly at 10% p.a. Find the time period (in months and years).

Solution — stepwise

  1. Let time = n months. P = ₹600, r = 10%. Total deposited = 600n.

  2. Interest formula simplifies here: I = 600 × [n(n+1) / 24] × 10/100 = 600 × [n(n+1) / 24] × 0.10 = 60 × [n(n+1) / 24] = (60/24) × n(n+1) = 2.5 × n(n+1).

  3. M.V. = total deposited + I = 600n + 2.5 n(n+1). Given M.V. = 24,930.

  4. Equation: 600n + 2.5 n(n+1) = 24,930. Multiply both sides by 2 to remove decimal: 1200n + 5 n(n+1) = 49,860.
    That is 5n^2 + 5n + 1200n − 49,860 = 0 ⇒ 5n^2 + 1205n − 49,860 = 0.

  5. Divide by 5: n^2 + 241n − 9,972 = 0. Solve quadratic:
    Discriminant D = 241^2 + 4 × 9,972 = 58,081 + 39,888 = 97,969 = 313^2.
    So n = [−241 ± 313] / 2. Positive root: n = (−241 + 313)/2 = 72/2 = 36 months.

  6. Therefore time = 36 months = 3 years.

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FAQs on Worksheet Solutions: Banking - Mathematics Class 10 ICSE

1. What are the main functions of banking in the economy?
Ans. Banking plays several critical roles in the economy, including accepting deposits, providing loans, facilitating payments, and offering financial services. Banks mobilize savings and channel them into productive investments, which helps in economic growth. They also provide a secure place for individuals and businesses to store their money while offering interest on deposits.
2. What is the difference between a commercial bank and a central bank?
Ans. A commercial bank is a financial institution that provides services such as accepting deposits, offering loans, and facilitating transactions for individuals and businesses. In contrast, a central bank is responsible for managing a country's monetary policy, regulating the banking system, and maintaining financial stability. The central bank also acts as a lender of last resort to commercial banks.
3. How do banks determine interest rates on loans?
Ans. Banks determine interest rates on loans based on several factors, including the cost of funds, the risk associated with the borrower, and prevailing market rates. The central bank's monetary policy also influences interest rates, as changes in the policy can affect the overall cost of borrowing in the economy. Additionally, banks may consider the creditworthiness of the borrower and the purpose of the loan when setting rates.
4. What is the significance of the Reserve Requirement in banking?
Ans. The Reserve Requirement is a regulation set by the central bank that determines the minimum amount of reserves a bank must hold against its deposits. This requirement is significant because it helps ensure that banks maintain liquidity to meet withdrawal demands while controlling the money supply in the economy. A higher reserve requirement can limit the amount of money banks can lend, while a lower requirement can encourage lending and investment.
5. What are the risks associated with banking operations?
Ans. Banks face several risks, including credit risk, which is the potential for borrowers to default on loans; liquidity risk, which arises when a bank cannot meet its short-term financial obligations; and operational risk, which includes losses from failed internal processes or systems. Additionally, banks are exposed to market risk due to fluctuations in interest rates and economic conditions, as well as reputational risk from public perception and trust.
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