Simple vs Compound Interest: The Difference, and the Formula

Two questions hide inside "the difference between simple and compound interest", and they want very different answers. An Indian student typing it usually needs a number, because the exam question reads "the difference between the compound interest and the simple interest on a sum for 2 years at 10% is Rs 500, find the sum." An American searching the same phrase usually wants to know which savings account to look at.

The pages that rank split the same way. Vedantu, CK-12 and Careers360 answer with formulas and practice questions. Thrivent, Saxo and a row of credit unions answer with product lists and a thirty-year chart. Neither set answers the other's question.

Both answers come from one idea, and the number that makes it concrete is this: on Rs 1,00,000 at 8%, the gap between the two is exactly zero after year one, and Rs 6,66,266 after year thirty.

What is the difference between simple and compound interest?

Simple interest is charged only on the original amount, while compound interest is charged on the original amount plus every rupee of interest added so far. That single change is why one grows in a straight line and the other curves.

Watch Rs 50,000 at 10% for three years. Simple interest earns Rs 5,000, then Rs 5,000, then Rs 5,000. Compound interest earns Rs 5,000, then Rs 5,500, then Rs 6,050, because year two is calculated on Rs 55,000 and year three on Rs 60,500.

	Simple interest	Compound interest
Interest is charged on	The original amount only	The original amount plus interest already added
Each year's interest	Identical every year	Larger every year
Shape of the growth	A straight line	A curve that steepens
Formula	SI = P x R x T / 100	A = P x (1 + R/100) to the power T
Where you meet it	Flat-rate loans, some short loans	Savings accounts, FDs, PPF, credit cards

The formula difference is one exponent. Everything else follows from it.

When does the gap actually open up?

The gap is exactly zero after the first year and grows slowly at first, which is why short comparisons make the two look almost the same. Time does the work here, and the rate only decides how fast.

On Rs 1,00,000 at 8%:

After	Simple interest	Compound interest	Gap
1 year	Rs 8,000	Rs 8,000	Rs 0
5 years	Rs 40,000	Rs 46,933	Rs 6,933
10 years	Rs 80,000	Rs 1,15,892	Rs 35,892
20 years	Rs 1,60,000	Rs 3,66,096	Rs 2,06,096
30 years	Rs 2,40,000	Rs 9,06,266	Rs 6,66,266

Read the first and last rows together. Same money, same rate, and the difference goes from nothing at all to more than six and a half times the original deposit. Nothing changed except how long it was left.

That first row is worth dwelling on because it kills a common misreading. Compound interest is not a better rate. For the first period it's the identical rate producing the identical number, and it only pulls ahead once there's accumulated interest for it to work on.

You can run either side on your own figures. Our simple interest calculator solves the straight-line version in any direction, and the compound interest calculator handles the curve, including what changes when compounding happens more often than once a year. The mechanics behind the curve are set out in compound interest explained.

How do you calculate the difference between CI and SI?

Over 2 years the difference between compound and simple interest is P x (R/100) squared, and over 3 years it is P x (R/100) squared x (300 + R)/100. These come out of the algebra rather than being rules to memorise, and they're what Indian exam questions on this topic are built around.

The 2-year version falls out quickly. Compound interest over two years is P(2r + r squared) where r is R/100, and simple interest is 2Pr. Subtract, the 2Pr cancels, and P x r squared is all that survives.

Principal and rate	Over 2 years	Over 3 years
Formula	P x (R/100)²	P x (R/100)² x (300 + R)/100
Rs 50,000 at 10%	Rs 500	Rs 1,550
Checked the long way	Rs 10,500 minus Rs 10,000	Rs 16,550 minus Rs 15,000

Both check out against the slow method, which is the point of showing them side by side.

The formulas also run backwards, and that's usually what the exam wants. Told that the 2-year difference is Rs 500 at 10%, rearrange to P = D divided by (R/100) squared, giving Rs 500 divided by 0.01, which is Rs 50,000. Vedantu ranks for several of these exact questions and its own topic page doesn't carry the shortcut, which is a strange gap in the page most Indian students land on.

Which accounts and loans use which?

Most things that pay you use compound interest and most things that sound cheap use simple interest, which is close to the opposite of what suits you. The label tells you less than the mechanism.

In India, RBI's Master Direction on interest rates for deposits requires interest on savings deposits to be calculated on a daily product basis and credited at quarterly or longer intervals. So a savings account works out interest on your end-of-day balance every day, then compounds it only four times a year at most. Fixed deposits usually compound quarterly. Public Provident Fund compounds once a year.

On the borrowing side the picture inverts. Flat-rate loans from vehicle dealers and some finance companies charge simple interest on the full original amount for the whole tenure, which sounds gentle and works out near double the quoted rate. Our simple interest guide goes through why a 10% flat rate is really about 17.9%.

American usage differs enough to confuse anyone reading across markets. There, auto loans, personal loans and most student loans are called simple interest loans, but the phrase means interest accrues on the outstanding balance, which is closer to what India calls reducing balance. Credit cards compound in both countries, which is the single most expensive place a person meets the idea.

Why is simple interest better when you borrow?

Compound interest helps you when you are saving and hurts you when you are borrowing, because the mechanism is indifferent to which direction the money is flowing. The same rule that grows a deposit grows a debt.

This is the part that maths classes tend to skip. Compound interest arrives as the harder chapter, so it registers as the better one, and people leave school with a vague sense that compound is good. It isn't good or bad. On a credit card balance it's the reason a balance you keep paying never seems to shrink, and there the compounding is monthly rather than yearly, which makes it sharper still.

My own view, and it's a view about how the idea is taught rather than about anyone's money: the asymmetry deserves to be the headline of the topic instead of a footnote at the end. A student who leaves the chapter knowing only that compound interest grows faster has learned the half that helps a saver and missed the half that protects a borrower.

What this post deliberately does not cover

This explains how the two kinds of interest differ, when the gap opens, and how to compute the difference between them. It isn't advice on where to keep your money, which account to open, or which loan to take.

It also leaves out compounding frequency in any depth, meaning what changes when interest compounds monthly or daily instead of yearly, along with continuous compounding, effective annual rate conversions, inflation-adjusted returns, and the tax treatment of interest income, which differs by product and by country. The worked examples assume annual compounding throughout and a rate that stays fixed, neither of which survives contact with a real floating-rate loan. For how a rate is set and reset in the first place, our interest rate explainer covers the benchmark rules. Anything touching your own tax position belongs with a chartered accountant.

Frequently asked questions

What is the difference between simple interest and compound interest?

Simple interest is calculated only on the original amount you put in or borrowed, so the interest is the same every year. Compound interest is calculated on the original amount plus all the interest added so far, so each year's interest is larger than the last. On Rs 50,000 at 10%, simple interest earns Rs 5,000 every single year, while compound interest earns Rs 5,000 in year one, Rs 5,500 in year two and Rs 6,050 in year three. Over one year the two are identical. The gap only appears from year two onward, and it widens the longer the money sits.

How do you calculate the difference between compound interest and simple interest?

For 2 years the difference is P x (R/100) squared, where P is the principal and R is the rate. For 3 years it is P x (R/100) squared x (300 + R)/100. On Rs 50,000 at 10%, the 2-year difference works out to Rs 500 and the 3-year difference to Rs 1,550, which you can check against the long way: compound interest of Rs 10,500 minus simple interest of Rs 10,000 is indeed Rs 500. The formulas also run backwards, so a stated 2-year difference of Rs 500 at 10% tells you the principal was Rs 50,000.

Which is better, simple interest or compound interest?

Neither is better on its own, because it depends entirely on which side of the money you are standing. When you are saving or investing, compound interest works for you and simple interest holds you back. When you are borrowing, that flips completely: simple interest costs you less and compound interest costs you more. This is why maths classes present compound interest as the more advanced idea while a borrower would rather never meet it.

Do Indian bank accounts pay simple or compound interest?

Compound, though less often than people assume. RBI's Master Direction on interest rates for deposits requires interest on savings deposits to be calculated on a daily product basis and credited at quarterly or longer intervals, so a savings account compounds at most four times a year despite the daily calculation. Fixed deposits in India are usually compounded quarterly. Public Provident Fund compounds once a year. Flat-rate loans from vehicle dealers and some finance companies run on simple interest, which sounds friendlier and usually is not.

Is compound interest always higher than simple interest?

It is never lower, and it is exactly equal for the first period. At the same rate on the same principal, one year of simple interest and one year of annually compounded interest give the identical figure, because there is no accumulated interest yet for the compounding to work on. From the second period onward compound interest pulls ahead and keeps pulling. The one case where compound interest is not higher is a rate of zero, where both produce nothing.

What is the formula for simple interest and compound interest?

Simple interest is SI = P x R x T / 100, and the total is A = P + SI. Compound interest is A = P x (1 + R/100) raised to the power T, and the interest alone is that amount minus P. American textbooks write the same two as I = P x r x t and A = P(1 + r/n) raised to nt, using the rate as a decimal and adding n for the number of compounding periods a year. The compound version has the exponent, which is the entire reason its line curves upward while the simple one stays straight.

Sources

• Reserve Bank of India, Master Direction on Interest Rate on Deposits (Co-operative Banks), sections 6 and 11 (savings deposit interest calculated on a daily product basis, credited at quarterly or longer intervals) rbi.org.in
• Reserve Bank of India, Master Direction on Interest Rate on Advances, 2016, paragraph 4(a)(vii) (interest on advances charged at monthly rests) rbi.org.in
• Consumer Financial Protection Bureau, What's the difference between a simple interest rate and precomputed interest on an auto loan? (the American usage, where simple interest accrues on the outstanding balance) consumerfinance.gov
• The difference formulas and every figure in the tables are our own derivations and calculations, each checked against the long method on the same principal and rate.