# Simple interest vs compound interest: the formulas, a side-by-side table, and why compounding frequency matters

> ₹1 lakh at 7 percent becomes ₹1.35 lakh with simple interest and ₹1.41 lakh with compound interest after five years, and the gap widens every year after that. Both formulas with worked numbers, what monthly, quarterly and daily compounding really change, the flat-rate loan trap, and the shortcut for school and exam questions.

Published 2026-10-22 by Toolcloak. 4 minute read. Original: https://toolcloak.com/articles/simple-interest-vs-compound-interest-the-formulas-a-side-by-side-table-and-why-compounding-frequency-matters
Related free tool: [Simple & Compound Interest Calculator](https://toolcloak.com/tools/interest-calculator)

Two people each put ₹1 lakh in an account paying 7 percent a year. One gets **simple interest**, the other **compound interest**. After one year their balances are identical. After thirty years one has ₹3.1 lakh and the other has ₹7.6 lakh. The only difference is whether the interest each year is allowed to earn interest of its own. That one idea sits under fixed deposits, loans, credit cards and every long-term investment.

> **In short**
> - **Simple interest = P × R × T ÷ 100.** It is always calculated on the original amount.
> - **Compound interest: A = P × (1 + r ÷ n)^(n × t).** Interest is added to the balance, then earns interest.
> - **The two match in year one and drift apart after that.** At 7%, ₹1 lakh is ₹2.4 lakh (simple) against ₹3.87 lakh (yearly compound) after 20 years.
> - **More frequent compounding helps, but only a little.** Quarterly, monthly and daily at 7% give 7.19%, 7.23% and 7.25% a year.

## The two formulas

**Same ₹1,00,000 at 7% for 5 years**

| Simple interest | Compound interest (yearly) |
| --- | --- |
| ₹1,35,000 | ₹1,40,255 |
| Interest = 1,00,000 × 7 × 5 ÷ 100 = ₹35,000 | Amount = 1,00,000 × 1.07^5 |
| The same ₹7,000 is added every year | Each year’s interest is bigger than the last |
| Grows in a straight line | Grows in a curve |

*The extra ₹5,255 is interest earned on earlier interest. With quarterly compounding, the five-year amount is ₹1,41,478.*

> **Formulas to keep:** Simple: Interest = P × R × T ÷ 100, and Amount = P + Interest.  Compound: Amount = P × (1 + r ÷ n)^(n × t), where r is the yearly rate as a decimal (7% = 0.07), n is how many times a year interest is added, and t is the number of years. Compound interest = Amount − P.

Try it: [Simple & Compound Interest Calculator](https://toolcloak.com/tools/interest-calculator). Choose simple or compound, set the compounding frequency, and see the maturity amount, the interest earned and how much extra compounding gives.

## The gap grows every year

In year one there is no difference at all, because there is no earlier interest to earn on. The difference shows up slowly and then fast. Here is ₹1 lakh at 7 percent, in lakh rupees.

**₹1 lakh at 7% a year: simple against compound (value in lakh rupees)**

|  | Compound (yearly) | Simple | Your original ₹1 lakh |
| --- | --- | --- | --- |
| Start | 1 | 1 | 1 |
| 5 yrs | 1.403 | 1.35 | 1 |
| 10 yrs | 1.967 | 1.7 | 1 |
| 15 yrs | 2.759 | 2.05 | 1 |
| 20 yrs | 3.87 | 2.4 | 1 |
| 25 yrs | 5.427 | 2.75 | 1 |
| 30 yrs | 7.612 | 3.1 | 1 |

*Touch a point to read the values. At 30 years, compound interest has produced more than two and a half times what simple interest has.*

| Years | Simple interest | Compound, yearly | Compound, quarterly | Compound, monthly |
| --- | --- | --- | --- | --- |
| 1 | ₹1,07,000 | ₹1,07,000 | ₹1,07,186 | ₹1,07,229 |
| 5 | ₹1,35,000 | ₹1,40,255 | ₹1,41,478 | ₹1,41,763 |
| 10 | ₹1,70,000 | ₹1,96,715 | ₹2,00,160 | ₹2,00,966 |
| 20 | ₹2,40,000 | ₹3,86,968 | ₹4,00,639 | ₹4,03,874 |
| 30 | ₹3,10,000 | ₹7,61,226 | ₹8,01,918 | ₹8,11,650 |

*₹1,00,000 at 7% a year. Years and amounts from the calculator’s formula.*

## Compounding frequency: how much does it matter?

A bank may say “7% compounded quarterly”. That means 1.75 percent is added to your balance every three months. Because you earn interest on interest sooner, you end the year slightly ahead of a plain 7 percent. The true yearly gain has a name: the **effective annual rate**.

**What a 7% stated rate really pays in a year**

|  | Effective annual rate |
| --- | --- |
| Yearly | 7.00% |
| Half-yearly | 7.12% |
| Quarterly | 7.19% |
| Monthly | 7.23% |
| Daily | 7.25% |

*Going from yearly to daily adds only 0.25 percentage points at 7%. The rate and the time you stay invested matter far more than the compounding schedule.*

- **Bank fixed deposits** in India typically compound quarterly, so the maturity is a touch above what simple interest would give. See [FD at 7%, after tax and inflation](https://toolcloak.com/articles/fd-at-7-percent-after-tax-and-inflation-what-you-actually-earn).
- **When comparing two schemes,** compare the effective annual rate, not the stated one, if they compound at different frequencies.
- **A higher rate beats faster compounding.** 8% yearly is better than 7% daily.

## How long to double: simple against compound

At 7 percent, simple interest adds ₹7,000 a year on ₹1 lakh, so it takes 100 ÷ 7 = **14.3 years** to double. With yearly compounding, doubling takes about **10.2 years**. The [rule of 72](https://toolcloak.com/articles/the-rule-of-72-how-long-money-takes-to-double) gives the same compound answer in your head: 72 ÷ 7 = 10.3.

**Years for ₹1 lakh to become ₹2 lakh at 7%**

|  | Value | Note |
| --- | --- | --- |
| Simple interest | 14.3 yrs | 100 ÷ 7 |
| Compound, yearly | 10.2 yrs | ln 2 ÷ ln 1.07 |
| Compound, quarterly | 10.0 yrs | A little faster again |

*That gap of four years is the whole case for letting interest stay invested. The guide on [starting at 25 or 35](https://toolcloak.com/articles/start-at-25-or-35-what-waiting-ten-years-really-costs) shows what it does over a career.*

## Where each one shows up in real life

| Where | Usually | What to know |
| --- | --- | --- |
| Bank fixed deposit, recurring deposit | Compound, often quarterly | Check the maturity amount; see the [RD guide](/articles/recurring-deposit-5000-a-month-for-5-years-how-the-maturity-is-worked-out) |
| PPF, EPF | Compound, credited yearly | Interest is added to the balance, so it grows the next year. See [PPF](/articles/ppf-15-years-of-1-5-lakh-a-year-what-you-end-up-with) and [EPF](/articles/epf-how-your-provident-fund-grows-over-30-years) |
| Mutual fund and share returns | Compounding by price growth | Compare with [CAGR](/articles/average-return-vs-cagr-why-20-percent-is-not-what-you-earned), not a simple average |
| Home and personal loans | Interest on the reducing balance | Early EMIs are mostly interest, see [loan amortization](/articles/loan-amortization-schedule-explained-why-early-emis-are-mostly-interest) |
| Credit card dues | Compounds on unpaid balance | See [the minimum payment trap](/articles/the-minimum-payment-trap-what-a-credit-card-balance-really-costs) |
| Informal loans, some bonds | Often simple | Agree in writing which one applies |

*Compound interest is your friend when you save and your enemy when you owe.*

## The flat-rate loan trap

Some personal, vehicle and consumer loans are advertised at a “flat” rate. Flat means simple interest on the **original** amount for the whole period, even though you repay part of it every month. A ₹1 lakh loan at 12 percent flat for 3 years adds ₹36,000 of interest. Total ₹1,36,000, divided into 36 equal payments, is about **₹3,778 a month**. The same EMI on a normal reducing-balance loan works out to an interest rate of about **21.2 percent a year**.

**The same ₹1 lakh loan, 3 years**

| “12% flat” | 12% reducing balance |
| --- | --- |
| ≈ 21.2% | 12% |
| Interest on the full ₹1 lakh for all 3 years | Interest only on what you still owe |
| EMI about ₹3,778 | EMI about ₹3,321 |
| True yearly cost of borrowing is almost double | What the headline rate really means |

*Always ask: is this rate flat or on the reducing balance? Then check the EMI with the [EMI guide](https://toolcloak.com/articles/your-emi-is-mostly-interest-for-the-first-decade).*

## For school and exam questions

Exam questions often ask for the **difference** between compound and simple interest, usually with yearly compounding. There is a shortcut that skips the long calculation.

- **For 2 years:** CI − SI = P × (R ÷ 100)². For ₹1,00,000 at 7%, it is 1,00,000 × 0.0049 = **₹490**.
- **For 3 years:** CI − SI = P × (R ÷ 100)² × (3 + R ÷ 100). For ₹1,00,000 at 7%, it is 1,00,000 × 0.0049 × 3.07 = **₹1,504**.
- **For months,** change time to years first: 6 months = 0.5 years, 9 months = 0.75 years. The calculator accepts decimals.
- **Always read what the question says** about compounding: yearly, half-yearly or quarterly. Half-yearly means n = 2 and the rate per period is half.

> **A habit worth building:** Before you commit to any scheme or loan, enter its numbers into the calculator twice: once as simple, once as compound. The difference tells you how much the answer depends on the type of interest. That is often more useful than the number itself.

## Frequently asked questions

### What is the difference between simple interest and compound interest?

Simple interest is always calculated on the original amount, so the same interest is added every period. Compound interest is calculated on the original amount plus the interest already earned, so it grows faster over time.

### Simple interest aur compound interest me kya fark hai?

Simple interest hamesha shuru ki rakam (principal) par lagta hai, isliye har saal same byaj milta hai. Compound interest me pichhle saal ka byaj bhi principal me jud jaata hai aur us par agle saal byaj lagta hai, isliye rakam tezi se badhti hai.

### What is the compound interest formula?

A = P × (1 + r ÷ n)^(n × t), where P is the principal, r the yearly rate as a decimal, n the number of times interest is compounded per year and t the years. Compound interest is A minus P.

### How do I calculate simple interest?

Multiply principal, rate and time, then divide by 100: SI = P × R × T ÷ 100. For ₹1,00,000 at 7% for 5 years it is 1,00,000 × 7 × 5 ÷ 100 = ₹35,000.

### Does monthly compounding give much more than yearly?

A little. At 7%, yearly compounding gives an effective 7.00 percent and monthly gives 7.23 percent. Over long periods the difference adds up, but the rate and the number of years matter much more.

### Do banks pay simple or compound interest on FDs?

Most fixed deposits in India compound interest, typically every quarter, when the interest is reinvested (cumulative). If you choose a payout option instead, the interest is paid out and does not compound. Check your bank’s terms.

### What does flat interest rate mean on a loan?

A flat rate charges interest on the original loan amount for the full period, even though the balance falls as you repay. This makes the true yearly cost much higher than the quoted rate. A 12 percent flat loan for 3 years is roughly 21 percent on a reducing balance.

### How do I find the difference between CI and SI for 2 years quickly?

Use P × (R ÷ 100)². For ₹1,00,000 at 7% with yearly compounding, the difference is 1,00,000 × 0.0049 = ₹490.