Key facts

  • The simple interest formula is SI = PRT/100, where P is principal, R is annual rate in percent, and T is time in years.
  • The annual compound amount formula is A = P(1 + R/100)^T when the rate is annual and compounding is once per year.
  • For exactly 2 years, the difference between compound interest and simple interest is P(R/100)^2.
  • Half-yearly compounding halves the annual rate and doubles the number of periods;

Key Points at a Glance

  1. 1

    Simple interest grows linearly because interest is calculated only on the original principal for every period.

  2. 2

    Compound interest grows faster than simple interest after the first compounding period because each period's interest becomes part of the next period's base.

  3. 3

    The simple interest formula is SI = PRT/100, where P is principal, R is annual rate in percent, and T is time in years.

  4. 4

    The annual compound amount formula is A = P(1 + R/100)^T when the rate is annual and compounding is once per year.

  5. 5

    For exactly 2 years, the difference between compound interest and simple interest is P(R/100)^2.

  6. 6

    Half-yearly compounding halves the annual rate and doubles the number of periods; quarterly compounding divides the rate by 4 and multiplies periods by 4.

  7. 7

    Discount questions use marked price as the base, while profit and loss questions use cost price as the base.

  8. 8

    Equal annual instalment questions can be solved by equating the present value or by moving all payments to the final date with compound-interest factors.

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Interest as a percentage of money and time

Interest is the extra amount paid for using money over time. In exam arithmetic, the lender, borrower, deposit, bank, shopkeeper or finance company may change, but the core variables stay fixed: principal, rate and time. Principal is the original sum. Rate is normally quoted per annum, so 8% means 8 rupees per year on every 100 rupees of principal unless the stem states another period. Time must be in years when the formula uses an annual rate.

The first exam discipline is base selection. Interest is not a random percentage of the final amount unless the question says so. If a person borrows Rs 20,000 at 9% per annum, the 9% is measured on Rs 20,000 under simple interest and on the current accumulated amount under compound interest. This distinction decides the whole question. A 6-month period becomes 1/2 year, 9 months becomes 3/4 year, and 18 months becomes 3/2 years when the rate is annual.

Rajasthan-linked practice can use farm loans, self-help group savings, small shop credit or coaching-fee instalments, but the computation remains the same. Fix the money base, convert the time, and only then apply the rate.

Exam cue: common wrong answers in this chapter begin with the right formula but the wrong base or time unit.

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