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Financial Management and Business Data Analytics · Time Value of Money

Simple Interest vs Compound Interest and Effective Rate

Updated 10 October 2026 · Fact-checked

Simple interest is earned only on the original principal: SI = P × r × n. Compound interest is earned on principal plus past interest: A = P(1 + r/m)^(mn). The effective annual rate converts any compounding frequency to a yearly rate: EAR = (1 + r/m)^m − 1. Compare rates only on an effective basis.

Understand Simple and Compound Interest

Interest is the price of using money for time. The two ways of calculating it differ in one thing: what the interest is charged on.

Simple interest is charged only on the original sum (the principal). Every year the interest is the same amount. If you invest ₹1,00,000 at 10% simple interest, you earn ₹10,000 every year, whether it is year 1 or year 5.

Compound interest is charged on the principal plus the interest already earned. Interest earns interest. At 10% compounded annually, year 1 interest is ₹10,000, but year 2 interest is on ₹1,10,000, so it is ₹11,000. The gap with simple interest widens each year. This is the base of all time value of money work.

Interest may be compounded more than once a year: half-yearly (m = 2), quarterly (m = 4), monthly (m = 12). The stated yearly rate is called the nominal rate. The more often you compound, the more you actually earn. The effective annual rate (EAR) is the rate that, compounded once a year, gives the same final amount. It lets you compare loans or deposits fairly.

For exactly one year, simple and compound interest give the same result when compounding is annual. For periods longer than one year, compound interest is higher at the same positive rate. For periods less than one year under annual compounding, simple interest is the usual convention.

Key rules to remember

Simple interest
SI = P × r × n
r is the annual rate as a decimal and n is in years. Convert months to years (9 months = 0.75).
Amount under simple interest
A = P × (1 + r × n)
Amount is principal plus interest.
Compound amount (annual)
A = P × (1 + r)^n
Compound interest = A − P.
Compound amount (m times a year)
A = P × (1 + r/m)^(m × n)
Rate per period is r/m and number of periods is m × n.
Effective annual rate
EAR = (1 + r/m)^m − 1
r is the nominal annual rate. For annual compounding EAR equals r.
Nominal rate from EAR
r = m × [(1 + EAR)^(1/m) − 1]
Use when the effective rate is given and you need the periodic or nominal rate.
Continuous compounding
A = P × e^(r × n); EAR = e^r − 1
e ≈ 2.71828. Use only when the question says continuous.

How to solve Simple and Compound Interest questions

Use this order for any simple or compound interest question. Most errors come from mismatching the rate and the period.

  1. 1Read whether the interest is simple or compound, and note P, the stated rate and the time.
  2. 2Note the compounding frequency (m). If none is stated for a deposit or loan, assume annual.
  3. 3Convert the rate and time to the same unit: periodic rate = r ÷ m and number of periods = m × n.
  4. 4Write the formula with the numbers substituted before calculating.
  5. 5Calculate the factor (1 + periodic rate)^periods, then multiply by P to get the amount.
  6. 6If compound interest is asked, subtract P from A. If EAR is asked, subtract 1 from the factor for one year and convert to a percentage.
  7. 7State the answer in rupees or per cent with the unit, and compare with the alternative if the question asks which is better.

Quickest way: Effective rate comparison shortcut

When to use it: Use when a question asks which of several offers (different rates and frequencies) is best, or asks for the effective rate.

  1. Compute EAR for each offer using (1 + r/m)^m − 1.
  2. Compare the EARs. The higher EAR is better for an investor and worse for a borrower.
  3. Only if the amount is needed, apply the winning EAR as an annual rate: A = P × (1 + EAR)^n.
  4. For small rates, remember that EAR is always higher than the nominal rate when m > 1, as a quick check on your answer.

Common mistakes in Simple and Compound Interest

  • Using the annual rate with the number of periods in quarters, or the reverse.

    Students plug r and n straight into the formula without adjusting for m.

    Fix: Always write r/m and m × n first. For 12% for 2 years compounded quarterly, use 3% and 8 periods.

  • Giving the amount when compound interest is asked.

    The formula A = P(1 + r)^n gives the total, and students stop there.

    Fix: Subtract the principal at the end. Compound interest = A − P.

  • Writing the EAR as (1 + r/m)^m without subtracting 1.

    Confusion between the growth factor and the rate.

    Fix: EAR is the factor minus 1. A factor of 1.1255 means an EAR of 12.55%.

  • Using months directly as years in simple interest.

    Rushing and forgetting the rate is per year.

    Fix: Convert first: 6 months = 0.5 year, 15 months = 1.25 years.

  • Dividing the rate by m but forgetting to multiply the periods by m.

    Only half of the adjustment is remembered.

    Fix: Apply both together. Check that the rate per period and the number of periods match.

  • Rounding the factor too early.

    Students round (1.03)^8 to two decimals to save time.

    Fix: Keep four to six decimals in the factor and round only the final rupee answer.

Worked examples

Example 1

Meera deposits ₹2,00,000 for 3 years at 9% per annum. Calculate the interest earned if (a) the interest is simple, and (b) the interest is compounded annually. Find the difference.

Show the solution
  1. (a) Simple interest = 2,00,000 × 0.09 × 3 = ₹54,000.
  2. (b) Amount = 2,00,000 × (1.09)^3.
  3. (1.09)^2 = 1.1881; (1.09)^3 = 1.295029.
  4. Amount = 2,00,000 × 1.295029 = ₹2,59,005.80.
  5. Compound interest = 2,59,005.80 − 2,00,000 = ₹59,005.80.
  6. Difference = 59,005.80 − 54,000 = ₹5,005.80.

Answer: Simple interest is ₹54,000 and compound interest is ₹59,005.80 (approx.). Compounding earns ₹5,005.80 more.

Example 2

A bank offers a fixed deposit at 12% per annum compounded quarterly. Find the effective annual rate. Also find the amount on ₹5,00,000 after 2 years.

Show the solution
  1. Periodic rate = 12% ÷ 4 = 3% = 0.03; m = 4.
  2. EAR = (1.03)^4 − 1.
  3. (1.03)^2 = 1.0609; (1.03)^4 = 1.0609 × 1.0609 = 1.12550881.
  4. EAR = 0.12550881, about 12.55%.
  5. For 2 years there are 8 quarters. (1.03)^8 = (1.12550881)^2 = 1.26677008.
  6. Amount = 5,00,000 × 1.26677008 = ₹6,33,385 (approx.).
  7. Check using EAR: (1.12550881)^2 gives the same factor, so the amount agrees.

Answer: EAR is about 12.55%. The amount after 2 years is about ₹6,33,385.

Exam tips

  • Write the periodic rate and number of periods on separate lines before any calculation. Examiners give step marks for the setup even if arithmetic slips.
  • In MCQs, check the frequency word (half-yearly, quarterly, monthly) first. Wrong options are usually built from the annual-compounding answer.
  • When a question gives compounding frequency for one option and not for another, compare them on EAR and show both EARs.
  • Show interest separately from amount. State clearly which one you are giving as the final answer.
  • If tables are given in the question, use the supplied factors. If not, compute powers by repeated squaring to save time.

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 calculated only on the original principal, so it is the same every year. Compound interest is calculated on the principal plus accumulated interest, so it grows each period. For more than one period at a positive rate, compound interest is larger.

What is the effective rate of interest formula with quarterly compounding?

EAR = (1 + r/4)^4 − 1, where r is the nominal annual rate as a decimal. For example, 8% nominal compounded quarterly gives (1.02)^4 − 1, which is about 8.24%.

How do I calculate the effective annual rate for any compounding frequency?

Divide the nominal rate by the number of compounding periods in a year, add 1, raise it to the power of that number, and subtract 1. Use m = 2 for half-yearly and m = 12 for monthly.

Is compound interest always better than simple interest?

For an investor, yes, when the period is longer than one compounding period and the rate is positive. For a borrower, it is the opposite, because compound interest costs more.