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Quantitative Aptitude · Mathematics of Finance

Simple Interest and Compound Interest for CA Foundation

Updated 1 October 2026 · Fact-checked

Simple interest is charged only on the original principal: SI = P × R × T ÷ 100. Compound interest is charged on principal plus earlier interest: A = P(1 + R/100)^n. For half-yearly or quarterly compounding, divide the rate by 2 or 4 and multiply the years by 2 or 4.

Understand Simple Interest and Compound Interest

Interest is the price of using money. If you lend ₹10,000, the borrower pays you extra for the time they keep it. The money you lend is the principal (P). The yearly percentage is the rate (R). The duration is the time (T or n).

In simple interest, interest is worked out on the original principal every year. It never changes. So interest is the same amount each year, and the total grows in a straight line.

In compound interest, interest earned in each period is added to the principal. The next period's interest is then charged on this bigger amount. This is interest on interest. So the total grows faster than in simple interest. In the first year both are equal. From the second year onward, compound interest is higher.

The compounding period is how often interest is added. It can be yearly, half-yearly (every 6 months) or quarterly (every 3 months). The more often it is added, the larger the amount. When the period is not a year, you work with the rate per period and the number of periods, not with years.

The amount (A) is principal plus interest. Many questions ask for the amount, but some ask only for the interest. Read the last line of the question before you start.

Key formulas to remember

Simple interest
SI = P × R × T ÷ 100
R is the rate per year in %. T must be in years. 9 months = 0.75 years.
Amount under simple interest
A = P + SI = P(1 + RT/100)
Use this when the question asks for the total repayable.
Amount under compound interest (yearly)
A = P(1 + R/100)^n
n is the number of years. Interest is added once a year.
Compound interest
CI = A − P
Always subtract the principal if the question asks for interest.
Compounding m times a year
A = P(1 + R/(100m))^(mn)
Half-yearly: m = 2. Quarterly: m = 4. Rate per period = R ÷ m. Periods = m × n.
CI − SI for 2 years
CI − SI = P(R/100)²
Valid for yearly compounding over exactly 2 years.
CI − SI for 3 years
CI − SI = P(R/100)² × (3 + R/100)
Valid for yearly compounding over exactly 3 years.
Effective annual rate
Effective rate = (1 + R/(100m))^m − 1
Gives the equivalent yearly rate when compounding is more than once a year.

How to solve Simple Interest and Compound Interest questions

Use this method for any simple or compound interest question. It prevents the usual slips with rate, time and the final subtraction.

  1. 1Identify the type: simple or compound. Look for words like 'compounded', 'interest on interest' or 'half-yearly'.
  2. 2Write down P, R, time and the compounding period. Note whether the question asks for amount or interest.
  3. 3Convert time to years if needed. For SI, use T in years directly.
  4. 4For compound interest, find the rate per period (R ÷ m) and the number of periods (m × years).
  5. 5Compute the multiplier (1 + rate per period/100) raised to the number of periods. Build it step by step if the power is 2 or 3.
  6. 6Multiply by P to get the amount A.
  7. 7If the question asks for interest, subtract P from A. For SI, use P × R × T ÷ 100 directly.
  8. 8Check that your answer is reasonable: CI must be above SI for more than one period, and A must be above P.

Quickest way: Multiplier method with option elimination

When to use it: Use it in the MCQ paper whenever the number of periods is 2, 3 or 4 and the rate is a round figure like 5%, 10% or 20%.

  1. Learn the multipliers: 5% → 1.05, 1.1025, 1.157625. 10% → 1.1, 1.21, 1.331, 1.4641. 20% → 1.2, 1.44, 1.728.
  2. Convert the rate and periods first (for half-yearly, halve the rate and double the periods), then pick the multiplier.
  3. Multiply P by the multiplier. This gives A in one step, and CI = A − P.
  4. Eliminate options before calculating fully. If CI is asked for 2 years, it must be greater than 2 years of SI.
  5. Check the last digit of the answer against the options. Often only one option fits.
  6. Skip the question if it needs a power of 5 or more with an awkward rate. Come back if time remains, since a wrong answer costs 0.25 marks.

Common mistakes in Simple Interest and Compound Interest

  • Using the full yearly rate for half-yearly or quarterly compounding.

    Students change the number of periods but forget to change the rate.

    Fix: Always change both together. Half-yearly: R ÷ 2 and n × 2. Quarterly: R ÷ 4 and n × 4.

  • Giving the amount when the question asks for compound interest.

    The formula gives A directly, and students stop there.

    Fix: Underline 'interest' or 'amount' in the question. For CI, subtract P as the last step.

  • Using the CI formula for simple interest, or the reverse.

    Both topics are in the same chapter and students rush the first line.

    Fix: Look for the word 'compound' or 'compounded'. If it is missing and nothing says interest is added to principal, treat it as simple.

  • Putting months into T without converting to years.

    The question says '9 months' and students write 9.

    Fix: Divide months by 12. 9 months = 9/12 = 0.75 years.

  • Calculating (1 + R/100)^n wrongly by multiplying the bracket by n.

    Students mix up a power with a multiplication.

    Fix: Multiply the bracket by itself n times. For n = 2, use 1.1 × 1.1 = 1.21, not 1.1 × 2.

  • Applying the CI − SI shortcut to the wrong number of years or to non-yearly compounding.

    The shortcut P(R/100)² is remembered without its condition.

    Fix: Use it only for exactly 2 years with yearly compounding. For other cases, work out CI and SI separately.

Worked examples

Example 1

Find the compound interest on ₹10,000 for 2 years at 10% per annum, compounded yearly. Options: (a) ₹2,000 (b) ₹2,100 (c) ₹2,200 (d) ₹2,310

Show the solution
  1. P = ₹10,000, R = 10%, n = 2 years, compounded yearly.
  2. A = 10,000 × (1.1)² = 10,000 × 1.21 = ₹12,100.
  3. CI = A − P = 12,100 − 10,000 = ₹2,100.
  4. Check: SI for 2 years would be ₹2,000, and CI must be higher. ₹2,100 fits.

Answer: (b) ₹2,100

Example 2

What is the amount on ₹16,000 for 1½ years at 20% per annum, compounded half-yearly? Options: (a) ₹20,800 (b) ₹21,296 (c) ₹21,600 (d) ₹22,000

Show the solution
  1. Compounding is half-yearly, so rate per period = 20 ÷ 2 = 10%.
  2. Number of periods = 1.5 × 2 = 3.
  3. Multiplier = (1.1)³ = 1.331.
  4. A = 16,000 × 1.331 = ₹21,296.
  5. Check: 16,000 × 1.331 = 16,000 + 16,000 × 0.331 = 16,000 + 5,296 = 21,296.

Answer: (b) ₹21,296

Example 3

The difference between compound interest and simple interest on a sum for 2 years at 5% per annum, compounded yearly, is ₹75. Find the sum. Options: (a) ₹20,000 (b) ₹25,000 (c) ₹30,000 (d) ₹36,000

Show the solution
  1. For 2 years with yearly compounding, CI − SI = P(R/100)².
  2. (R/100)² = (0.05)² = 0.0025.
  3. So P × 0.0025 = 75.
  4. P = 75 ÷ 0.0025 = 30,000.
  5. Check: SI = 30,000 × 5 × 2 ÷ 100 = ₹3,000. CI = 30,000 × 1.1025 − 30,000 = 33,075 − 30,000 = ₹3,075. Difference = ₹75.

Answer: (c) ₹30,000

Exam tips

  • Questions on this topic are usually direct. Practise the multipliers for 5%, 10% and 20% so that powers take seconds.
  • Read whether the compounding is yearly, half-yearly or quarterly before anything else. Examiners often set a trap option that uses the wrong period.
  • Check what is asked: amount, interest, principal or rate. Wrong options are often the amount when interest is asked.
  • Use CI − SI formulas to find an unknown principal quickly, but only for 2 or 3 years of yearly compounding.
  • If a question needs a long power at an awkward rate, leave it for the end. A wrong guess costs 0.25 marks.

Practice questions from Mathematics of Finance

Simple Interest and Compound Interest: frequently asked questions

What is the difference between simple interest and compound interest?

Simple interest is calculated only on the original principal, so it is the same each year. Compound interest is calculated on principal plus interest already earned, so it grows each period. For more than one period, compound interest is higher.

How do I calculate compound interest half-yearly or quarterly?

Divide the yearly rate by the number of compounding periods in a year, and multiply the number of years by the same number. For half-yearly, use R ÷ 2 and 2n. For quarterly, use R ÷ 4 and 4n. Then apply A = P(1 + rate per period/100)^periods.

Is the first year's interest the same under simple and compound interest?

Yes, if compounding is yearly. In the first year, interest is charged only on the principal in both cases. The difference starts from the second year.

Do I need a calculator for compound interest in CA Foundation?

You cannot rely on a calculator in the exam hall, so questions are designed with friendly numbers. Learn common multipliers like 1.1² = 1.21 and 1.05² = 1.1025, and you can do most questions by hand.