Compound Interest

“Compound Interest is a crucial concept in finance and banking, where the interest is calculated on both the initial principal and the accumulated interest over time.”

1. Basic Concepts and Formulas

  • Compound Interest (CI) = P × [(1 + R/100)^T – 1]
  • Amount (A) = P × (1 + R/100)^T
  • Principal (P) = A / (1 + R/100)^T
  • Rate (R) = [(A/P)^(1/T) – 1] × 100
  • Time (T) = log(A / P) / log(1 + R/100)

2. Type-Wise Questions

  • Type 1: Calculate Compound Interest
    Example: Find the compound interest on ₹5000 for 2 years at 10% per annum.
    Solution: CI = 5000 × [(1 + 10/100)^2 – 1] = ₹1050
  • Type 2: Find Amount after Compound Interest
    Example: If ₹5000 is invested at 10% for 2 years, what will be the total amount?
    Solution: A = 5000 × (1 + 10/100)^2 = ₹6050
  • Type 3: Find Principal
    Example: The amount is ₹12100 after 2 years, and the rate is 10%. Find the principal.
    Solution: P = 12100 / (1 + 10/100)^2 = ₹10000
  • Type 4: Calculate Time for Compound Interest
    Example: If the principal is ₹10000, the amount is ₹12100, and the rate is 10%, calculate the time.
    Solution: T = log(12100 / 10000) / log(1 + 10/100) = 2 years
  • Type 5: Find Rate from Amount and Time
    Example: The amount is ₹2200 after 2 years on a principal of ₹2000. Find the rate.
    Solution: R = [(2200/2000)^(1/2) – 1] × 100 = 10%
  • Type 6: Compound Interest for Half-Yearly or Quarterly Interest
    Example: Calculate the compound interest on ₹4000 at 10% per annum for 1 year, compounded half-yearly.
    Solution: CI = 4000 × [(1 + 10/200)^2 – 1] = ₹4080
  • Type 7: Compound Interest for Quarterly Interest
    Example: Calculate the compound interest on ₹5000 for 1 year at 12% per annum, compounded quarterly.
    Solution: CI = 5000 × [(1 + 12/400)^4 – 1] = ₹618.09
  • Type 8: Compound Interest for Different Periods
    Example: Calculate the compound interest on ₹2000 for 3 years at 8% per annum, compounded annually.
    Solution: CI = 2000 × [(1 + 8/100)^3 – 1] = ₹512.64
  • Type 9: Compound Interest with Different Time Periods
    Example: ₹5000 is invested for 3 years at 12% compounded annually. Find the compound interest.
    Solution: CI = 5000 × [(1 + 12/100)^3 – 1] = ₹1881.6
  • Type 10: Find Amount on Compound Interest
    Example: A sum of ₹12000 is invested for 2 years at 8% per annum compounded annually. Find the amount.
    Solution: A = 12000 × (1 + 8/100)^2 = ₹14060.80
  • Type 11: Compound Interest with Monthly Compounding
    Example: ₹1500 is invested for 1 year at 10% interest compounded monthly. Find the compound interest.
    Solution: CI = 1500 × [(1 + 10/1200)^12 – 1] = ₹157.62
  • Type 12: Compound Interest for 2 Periods
    Example: ₹10000 is invested at 10% for 2 years, compounded quarterly. Find the compound interest.
    Solution: CI = 10000 × [(1 + 10/400)^8 – 1] = ₹2104.71
  • Type 13: Compound Interest with Mixed Time Periods
    Example: ₹5000 is invested at 12% for 1 year compounded quarterly, and for 2 years compounded annually. Find the total amount.
    Solution: CI = 5000 × [(1 + 12/400)^4 – 1] = ₹619.99 + further compound for next year.
  • Type 14: Compound Interest for Non-Annual Compounding
    Example: ₹2500 is invested for 3 years at 8% per annum, compounded monthly. Calculate the amount.
    Solution: A = 2500 × (1 + 8/1200)^36 = ₹3154.70
  • Type 15: Compound Interest for Fixed Interval
    Example: ₹2000 is invested at 15% compounded semi-annually for 2 years. Find the amount.
    Solution: A = 2000 × (1 + 15/200)^4 = ₹2304.68
  • Type 16: Find the Total Compound Interest
    Example: ₹10000 is invested for 2 years at 5% compounded annually. Find the compound interest.
    Solution: CI = 10000 × [(1 + 5/100)^2 – 1] = ₹1025

3. Tips to Remember

  • Always use the compound interest formula based on the compounding frequency (quarterly, monthly, annually).
  • Be careful while converting the rate and time to match the compounding frequency.
  • Compound interest leads to higher earnings as the interest is calculated on accumulated interest.
  • Remember that compound interest grows exponentially over time, unlike simple interest.
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