NISM-Series-X-A: Investment Adviser (Level 1) · Time Value of Money

Simple and Compound Interest for NISM Investment Adviser Level 1

Updated 11 October 2026 · Fact-checked

Simple interest is earned on the original principal only. Compound interest is earned on principal plus interest already added. Use SI = P × r × t and A = P × (1 + r/m)^(m×t). To compare rates with different compounding, convert each to the effective annual rate: EAR = (1 + r/m)^m − 1.

Understand Simple and Compound Interest

Interest is the price of using money for time. The question is: on what amount is interest calculated each period?

With simple interest, interest is always calculated on the original principal. If you invest ₹1,00,000 at 10% a year, you earn ₹10,000 every year. The interest earned does not itself earn anything. The growth is a straight line.

With compound interest, interest is added to the balance and the next period's interest is calculated on the larger amount. This is "interest on interest". The growth curves upward. The longer the time and the higher the rate, the bigger the gap from simple interest. In year 1 both methods give the same interest. The gap appears from year 2 onwards.

Compounding frequency is how often interest is added: yearly, half-yearly, quarterly, monthly or daily. The quoted annual rate is the nominal rate. If compounding is more frequent than yearly, you earn more than the nominal rate. The true yearly return is the effective annual rate (EAR). For yearly compounding, EAR equals the nominal rate. For more frequent compounding, EAR is higher. Use EAR to compare two investments or loans that compound differently.

Key formulas to remember

Simple interest: SI = P × r × t; r is the annual rate as a decimal and t is in years. Convert months to years (9 months = 0.75 year).
Amount under simple interest: A = P × (1 + r × t); A is principal plus interest.
Compound amount (annual compounding): A = P × (1 + r)^t; Compound interest = A − P.
Compound amount (m times a year): A = P × (1 + r ÷ m)^(m × t); m = 2 for half-yearly, 4 for quarterly, 12 for monthly. Periodic rate is r ÷ m and number of periods is m × t.
Effective annual rate: EAR = (1 + r ÷ m)^m − 1; r is the nominal annual rate as a decimal. EAR is greater than r when m > 1 and r > 0.
Continuous compounding: A = P × e^(r × t); Limit as m becomes very large. e ≈ 2.71828. EAR = e^r − 1.

How to solve Simple and Compound Interest questions

Use this order for any simple or compound interest question. It stops most errors on rate, time and frequency.

1Identify whether the question says simple or compound. If it says nothing about simple interest and mentions compounding or growth, use compound.
2Write down P, the nominal annual rate r, the time in years t, and the compounding frequency m.
3Convert the rate to a decimal and make time and rate use the same unit (years).
4For compound interest, calculate the periodic rate r ÷ m and the number of periods m × t.
5Apply the formula and compute the amount A. Subtract P if the question asks for interest.
6If the question compares options, compute EAR for each and compare them, not the nominal rates.
7Check the answer for sense: compound interest must be at least simple interest for the same rate and time (t > 1), and EAR must be at least the nominal rate.

Quickest way: Estimate and eliminate

When to use it: Use when the options are far apart and you have limited time per question.

Compute simple interest first. It is quick and gives a floor for the answer.
Compound interest must be above this floor. Remove any option below it.
For short periods, compound interest is only slightly above simple. For long periods or high rates, the gap is large.
For EAR questions, remember more frequent compounding means a higher EAR. Rank options by frequency if the nominal rate is the same.
Do the full calculation only for the two options that remain.

Common mistakes in Simple and Compound Interest

Using the nominal rate directly when compounding is half-yearly, quarterly or monthly.
Students plug 12% into the formula and forget it is an annual rate.
Fix: Always divide the rate by m and multiply the years by m. Monthly at 12% means 1% for each of 12 periods per year.
Treating compound interest as the amount, or the amount as the interest.
The formula gives A, which includes principal.
Fix: Read the last line of the question. If it asks for interest, subtract P from A.
Using months as t in a formula with an annual rate.
The question gives a period such as 18 months.
Fix: Convert to years (1.5) or use the periodic rate with the number of periods. Keep units consistent.
Comparing nominal rates of investments that compound differently.
The headline rate looks like the return.
Fix: Convert each to EAR and compare. Nominal rates are comparable only when compounding frequency is the same.
Assuming compound interest is higher in the first year.
Students think compounding always gives more at every point.
Fix: With yearly compounding, year-1 interest is identical to simple interest. Higher interest appears only when interest is credited before the period ends or after year 1.
Calculating EAR as (1 + r ÷ m)^m without subtracting 1.
The expression looks like a rate but is a growth factor.
Fix: Subtract 1 and then express as a percentage.

Worked examples

Example 1

₹2,00,000 is invested for 2 years at 10% a year. Compare the interest earned under simple interest and under annual compounding. What is the difference?

Show the solution

Simple interest = 2,00,000 × 0.10 × 2 = ₹40,000.
Compound amount = 2,00,000 × (1.10)^2 = 2,00,000 × 1.21 = ₹2,42,000.
Compound interest = 2,42,000 − 2,00,000 = ₹42,000.
Difference = 42,000 − 40,000 = ₹2,000.
Check: the extra ₹2,000 is the interest on year-1 interest: 10% of ₹20,000 = ₹2,000.

Answer: Simple interest is ₹40,000, compound interest is ₹42,000, and the difference is ₹2,000.

Example 2

Bank A offers 12% a year compounded quarterly. Bank B offers 12.5% a year compounded annually. Which gives the higher effective annual rate?

Show the solution

Bank A: periodic rate = 12% ÷ 4 = 3% = 0.03, with m = 4.
EAR of A = (1.03)^4 − 1.
(1.03)^2 = 1.0609. (1.0609)^2 = 1.12550881.
EAR of A = 0.12550881, which is about 12.55%.
Bank B compounds annually, so its EAR equals its nominal rate, 12.5%.
Compare: 12.55% is higher than 12.50%.

Answer: Bank A is better, with an EAR of about 12.55% against 12.5% for Bank B.

Exam tips

Look for the words "compounded" and the frequency in the question. A missed frequency is the most common trap.
Expect EAR comparison questions. The option with more frequent compounding at the same nominal rate has the higher EAR.
Treat the rate as annual unless stated otherwise, and check whether time is in months or years.
Wrong answers cost marks on X-A, and 2-mark caselet questions cost twice as much as 1-mark ones. Use the floor check to avoid guessing on calculation questions.
Keep calculator steps tidy: compute the growth factor first, then multiply by P.

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 amount every period. Compound interest is calculated on principal plus accumulated interest, so it grows each period. Over more than one year, compound interest is higher at the same rate.

What is the effective annual rate formula with compounding frequency?

EAR = (1 + r ÷ m)^m − 1, where r is the nominal annual rate as a decimal and m is the number of compounding periods per year. For example, 12% compounded monthly gives (1.01)^12 − 1, which is about 12.68%.

Does more frequent compounding always increase the return?

At a positive nominal rate, yes. Monthly compounding gives a higher EAR than quarterly, which gives more than yearly. The increase gets smaller as frequency rises, and it is bounded by continuous compounding.

When is EAR equal to the nominal rate?

When interest is compounded once a year (m = 1). The nominal rate and the effective rate are then the same.