Fundamentals of Business Mathematics and Statistics · Time Value of Money and Annuity - Simple and Compound Interest

Simple Interest Formula and Problems for CMA Foundation

Updated 10 October 2026 · Fact-checked

Simple interest is interest charged only on the original principal, so it is the same every year. Use SI = P × R × T ÷ 100, where R is the yearly rate in % and T is time in years. Amount = P + SI. Rearrange the formula to find P, R or T.

Understand Simple Interest

When you lend or borrow money, the lender charges a fee for its use. That fee is interest. The money you start with is the principal. The rate tells you how much interest is charged for each ₹100 per year. The time is how long the money is used.

In simple interest, interest is worked out only on the original principal. Interest already earned does not earn more interest. So the interest for every year is the same. If ₹10,000 earns ₹800 in year 1, it earns ₹800 in year 2 and ₹800 in year 3.

This is why simple interest grows in a straight line. Total interest is directly proportional to principal, rate and time. Double any one of them and the interest doubles, if the others stay fixed.

The amount is what you get back at the end: principal plus interest. Most MCQs ask for one of five things: interest, amount, principal, rate or time. Every one of them comes from the same formula.

Unless the question says otherwise, the rate is per annum (per year). If time is given in months or days, convert it to years before you use the formula.

Key formulas to remember

Simple interest: SI = P × R × T ÷ 100; P is principal in ₹, R is rate per annum in %, T is time in years.
Amount: A = P + SI = P × (1 + R × T ÷ 100); Amount is the total repaid at the end of the period.
Principal: P = SI × 100 ÷ (R × T); Use when interest, rate and time are known. If amount is given, first find SI = A − P or use P = A ÷ (1 + RT ÷ 100).
Rate: R = SI × 100 ÷ (P × T); Answer is in % per annum when T is in years.
Time: T = SI × 100 ÷ (P × R); Answer is in years. Multiply by 12 for months.
Time conversion: Months ÷ 12 = years; Days ÷ 365 = years; Use the conversion the question implies. Most exam problems use clean values like 6 months = 0.5 year.

How to solve Simple Interest questions

Use this method for any simple interest question. It stops you from mixing units.

1Read the question and mark what is asked: SI, amount, P, R or T.
2Write down the given values and check whether the amount or the interest is given.
3Convert time to years and make sure the rate is per annum.
4Pick the formula that has your unknown on one side, such as SI = PRT ÷ 100.
5If the amount is given instead of interest, use SI = Amount − P or A = P(1 + RT ÷ 100).
6Substitute the values and cancel zeros before multiplying.
7Check the unit of the answer (₹, % or years) and match it with the options.

Quickest way: Per-year interest shortcut

When to use it: Use it when the numbers are round and you want the answer in a few seconds.

Find one year's interest first: P × R ÷ 100. For ₹20,000 at 6%, this is ₹1,200.
Multiply by the number of years to get SI.
For amount, add P to the SI.
For rate or time, divide the total SI by the interest of one year at 1%, which is P ÷ 100. For example, SI ₹2,400 on ₹10,000: 1% gives ₹100 a year, so R × T = 24.
Use R × T = 24 to test options. It works for 6% for 4 years, 8% for 3 years and so on, so pick the one that matches the question.

Common mistakes in Simple Interest

Using months directly as T
Students see 'for 9 months' and plug in 9.
Fix: Divide by 12 first. 9 months = 0.75 year.
Giving SI when the question asks for the amount
The calculation ends at SI and the student rushes to mark the option.
Fix: Underline the word 'amount' or 'total repaid'. Add the principal to the SI.
Forgetting to divide by 100
The rate is treated as 8 instead of 8%.
Fix: Always keep ÷ 100 in the formula. Write SI = P × R × T ÷ 100 every time.
Using the amount as the principal when finding the rate
The question gives the sum after some years, and the student puts it in P.
Fix: Find SI = Amount − Principal first, then use R = SI × 100 ÷ (P × T).
Mixing a half-yearly or quarterly rate with a yearly time
A rate given for a part of the year is used as if it were per annum.
Fix: Convert the rate to per annum (for example, 2% per quarter = 8% per annum) before substituting.

Worked examples

Example 1

Mr Sharma borrows ₹50,000 at 8% per annum simple interest for 2 years 6 months. How much does he repay in total? Options: (a) ₹60,000 (b) ₹10,000 (c) ₹58,000 (d) ₹62,000

Show the solution

P = ₹50,000, R = 8%, T = 2 years 6 months = 2.5 years.
SI = 50,000 × 8 × 2.5 ÷ 100.
50,000 ÷ 100 = 500. Then 500 × 8 = 4,000. Then 4,000 × 2.5 = 10,000.
SI = ₹10,000.
The question asks for the total repaid, which is the amount.
Amount = 50,000 + 10,000 = ₹60,000.

Answer: (a) ₹60,000. Option (b) is only the interest.

Example 2

A sum of money amounts to ₹13,200 in 4 years and to ₹14,400 in 6 years at simple interest. Find the sum. Options: (a) ₹10,000 (b) ₹10,800 (c) ₹12,000 (d) ₹9,600

Show the solution

Simple interest is the same every year, so the difference in amounts is the interest for the extra years.
Extra time = 6 − 4 = 2 years. Extra interest = 14,400 − 13,200 = ₹1,200.
Interest for 1 year = 1,200 ÷ 2 = ₹600.
Interest for 4 years = 600 × 4 = ₹2,400.
Principal = Amount after 4 years − interest for 4 years = 13,200 − 2,400 = ₹10,800.
Check: 10,800 + 600 × 6 = 10,800 + 3,600 = 14,400, which matches the data.

Answer: (b) ₹10,800.

Exam tips

Convert time and rate to years and per annum before anything else. Most wrong answers come from units.
For questions with two amounts at two times, subtract them to get the yearly interest, then work back to the principal.
Cancel zeros before multiplying. With round numbers, the answer should come in under 30 seconds.
Check whether the option list contains the interest as a trap next to the amount.
There is no negative marking, so if you are short on time, eliminate options that are clearly too small or too large and still mark an answer.

Practice questions from Time Value of Money and Annuity - Simple and Compound Interest

Simple 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 Interest: frequently asked questions

What is the simple interest formula for CMA Foundation?

SI = P × R × T ÷ 100, where P is the principal, R is the rate per annum in % and T is the time in years. The amount is P + SI. Every other form is a rearrangement of this one.

How do I find the principal when the amount is given?

Use P = A ÷ (1 + R × T ÷ 100). Or find SI = A − P by working in terms of the unknown. For two amounts at two times, subtract them to get the yearly interest, then work back to the principal.

What is the difference between simple and compound interest?

In simple interest, interest is charged only on the original principal, so it is equal every year. In compound interest, interest is added to the principal and then earns interest as well. Simple interest grows in a straight line and compound interest grows faster.

How do I handle time in months or days?

Convert it to years. Divide months by 12 and days by 365 unless the question gives a different basis. For example, 18 months is 1.5 years.