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Corporate Accounting and Financial Management · Time Value of Money

Simple Interest and Compound Interest: Formulas and Method

Updated 11 October 2026 · Fact-checked

Simple interest is charged only on the original principal: SI = P × r × n. Compound interest is charged on principal plus earlier interest: A = P(1 + r/m)^(mn). To solve a question, match the rate period to the compounding period, compute the amount, then subtract principal. The effective rate converts any nominal rate to an annual equivalent.

Understand Simple and Compound Interest

Interest is the price of using money for time. If you lend ₹1,00,000, you expect more back. The extra amount is interest. The two basic methods differ in what they charge interest on.

Under simple interest, interest is calculated only on the original principal. Every year the interest is the same. Interest of 10% on ₹1,00,000 is ₹10,000 each year, whether it is year 1 or year 5.

Under compound interest, interest is added to the principal at the end of each compounding period. The next period's interest is then charged on this bigger amount. This is interest on interest. So money grows faster than under simple interest, and the gap widens with time.

Compounding need not be yearly. It can be half-yearly (m = 2), quarterly (m = 4) or monthly (m = 12). The stated annual rate is the nominal rate. More frequent compounding gives a higher return than the nominal rate. The effective rate is the annual rate that gives the same final amount as the nominal rate with its compounding. It is the fair figure for comparing two offers.

This topic is the base of Time Value of Money. Future value, present value and annuities all build on compound growth. Get this right and the later topics become easier.

Key rules to remember

Simple interest
SI = P × r × n
r is the annual rate as a decimal (10% = 0.10) and n is time in years. Interest is the same every year.
Amount under simple interest
A = P + SI = P(1 + r × n)
Growth is a straight line over time.
Amount under compound interest (yearly)
A = P(1 + r)^n
Compound interest = A − P.
Amount with m compounding periods a year
A = P(1 + r/m)^(m × n)
m = 2 for half-yearly, 4 for quarterly, 12 for monthly. Use the periodic rate r/m and the number of periods m × n.
Effective rate of interest
EAR = (1 + r/m)^m − 1
r is the nominal annual rate as a decimal. If m = 1, the effective rate equals the nominal rate.
Compound interest
CI = P[(1 + r/m)^(m × n) − 1]
Gives interest directly without finding the amount first.
Present sum from amount
P = A ÷ (1 + r/m)^(m × n)
Used when the final amount is known and the starting sum is needed.

How to solve Simple and Compound Interest questions

Use this method for any simple or compound interest question. It stops you mixing up rates and periods.

  1. 1Read the question and decide the method: simple or compound. If it says nothing, check the context; in this chapter, assume compound only when stated.
  2. 2Write down P, the annual rate r, the time in years n, and the compounding frequency m.
  3. 3Convert the rate to a decimal and find the periodic rate: r ÷ m.
  4. 4Find the number of periods: m × n. Convert months to years first (9 months = 0.75 year).
  5. 5Put the values in the correct formula and calculate the amount A.
  6. 6Subtract P if the question asks for interest, not the amount.
  7. 7If the question asks for the effective rate, use (1 + r/m)^m − 1 and show it as a percentage.
  8. 8Write the answer with units in rupees or per cent, and check that it is sensible: compound interest should be at least simple interest.

Quickest way: Build up year by year for short periods

When to use it: Use when the period is two or three compounding periods and no calculator tables are given. It is fast and easy to check.

  1. Find the periodic rate and number of periods.
  2. Multiply the principal by (1 + periodic rate) once for each period.
  3. Write the balance after each period, so a mistake is easy to spot.
  4. Subtract the principal for interest.
  5. For comparison with simple interest, remember simple interest for 2 years is just 2 × first-year interest. The difference between CI and SI for 2 years is P × (r)^2 for yearly compounding.

Common mistakes in Simple and Compound Interest

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

    Students copy the rate from the question and forget it applies per year only.

    Fix: Always divide the annual rate by m and multiply the years by m before using the formula.

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

    The formula gives A, and students stop there.

    Fix: Re-read the last line of the question. Subtract P to get interest.

  • Writing the rate as 10 instead of 0.10 in the formula.

    Per cent form is used in simple interest shortcuts like PRN ÷ 100.

    Fix: Convert to a decimal first, or use the form P × r × n ÷ 100 consistently for simple interest only.

  • Treating the nominal rate as the effective rate.

    Students assume 12% compounded monthly means 12% a year.

    Fix: Compute (1 + r/m)^m − 1. Effective rate is higher than nominal when m is more than 1.

  • Not converting months to years.

    The time is given as 18 months and is put directly as n.

    Fix: Divide months by 12. Then multiply by m for the number of periods.

  • Rounding the periodic factor too early.

    Students round (1.05)^4 to a short value and lose accuracy.

    Fix: Keep at least four decimals during working. Round only the final answer.

Worked examples

Example 1

Find the simple interest and the compound interest on ₹50,000 for 2 years at 10% per annum, with yearly compounding. Also find the difference.

Show the solution
  1. Simple interest = 50,000 × 0.10 × 2 = ₹10,000.
  2. Compound amount = 50,000 × (1.10)^2 = 50,000 × 1.21 = ₹60,500.
  3. Compound interest = 60,500 − 50,000 = ₹10,500.
  4. Difference = 10,500 − 10,000 = ₹500.
  5. Check: difference = P × r^2 = 50,000 × 0.01 = ₹500.

Answer: Simple interest is ₹10,000, compound interest is ₹10,500, and the difference is ₹500.

Example 2

Mehta Traders deposits ₹2,00,000 at 12% per annum compounded half-yearly for 1 year. Find the amount and the effective rate of interest.

Show the solution
  1. P = ₹2,00,000, r = 12% = 0.12, m = 2, n = 1.
  2. Periodic rate = 0.12 ÷ 2 = 0.06. Number of periods = 2 × 1 = 2.
  3. Amount = 2,00,000 × (1.06)^2 = 2,00,000 × 1.1236 = ₹2,24,720.
  4. Interest earned = 2,24,720 − 2,00,000 = ₹24,720.
  5. Effective rate = (1.06)^2 − 1 = 1.1236 − 1 = 0.1236, that is 12.36%.
  6. Check: 24,720 ÷ 2,00,000 = 0.1236, which agrees.

Answer: The amount is ₹2,24,720 and the effective rate of interest is 12.36% per annum.

Exam tips

  • Write the formula, then the substituted values, then the answer. Marks are given for method even if arithmetic slips.
  • Always state the periodic rate and the number of periods in a separate line. This shows the examiner you handled compounding correctly.
  • If the question gives no tables, keep numbers simple and compute step by step. Do not leave powers unsolved.
  • For effective rate questions, show the result as a percentage and compare it with the nominal rate in one line.
  • Check that compound interest is not less than simple interest for the same inputs. It is a quick sense check.

Practice questions from Time Value of Money

Simple and Compound Interest in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Simple and Compound Interest: frequently asked questions

What is the difference between simple interest and compound interest?

Simple interest is charged only on the original principal, so it is the same every year. Compound interest is charged on principal plus interest already added, so it grows each period. For the same rate and time, compound interest is higher when time is more than one period.

How do I calculate compound interest with half-yearly compounding?

Halve the annual rate and double the number of years. Then use A = P(1 + r/2)^(2n). For 12% for 3 years, use 6% for 6 periods. Subtract P to get the interest.

What is the effective rate of interest formula?

Effective rate = (1 + r/m)^m − 1, where r is the nominal annual rate as a decimal and m is the number of compounding periods a year. For 12% compounded quarterly it is (1.03)^4 − 1, about 12.55%.

Is the effective rate always higher than the nominal rate?

It is higher when interest is compounded more than once a year. If compounding is yearly, both are equal. The more often interest compounds, the larger the gap.