Simple interest calculator:
how it differs from compound growth

Simple interest formula and how to use it

Interest is the price of using money for a period. You earn it when you lend or deposit, and pay it when you borrow. Three things set its size: how much, how long and at what rate.

Simple interest is calculated only on the original amount. Interest that has already been earned does not earn further interest, so the same rupee amount is added every year.

The formula can also be rearranged when one of the three inputs is unknown:

• Rate: r = Interest ÷ (P × t)
• Time: t = Interest ÷ (P × r)
• Principal: P = Interest ÷ (r × t)

As an example, if ₹80,000 earns ₹12,000 over 2 years, the rate is 12,000 ÷ (80,000 × 2) = 0.075, which is 7.5% a year.

1. 1Convert the rate to a decimal by dividing by 100.
2. 2Express the time in years, using fractions for months: 18 months is 1.5 years.
3. 3Multiply principal, rate and time to get the interest.
4. 4Add the interest to the principal for the total amount.

Worked example: ₹1,00,000 at 8% for 5 years

For short periods, express the time as a fraction of a year. Interest on ₹50,000 at an assumed 9% for 90 days is ₹50,000 × 0.09 × 90 ÷ 365 = ₹1,109.59.

Be careful when a loan is quoted as a 'flat' rate, which is simple interest on the original amount for the whole term. A ₹1,00,000 loan at a flat 10% for 3 years carries ₹30,000 of interest, and the monthly instalment is ₹3,611. Because you repay principal every month, the equivalent reducing-balance rate is about 17.9% a year, far above the headline 10%.

Months work the same way. Interest on ₹60,000 at an assumed 7% for 18 months is ₹60,000 × 0.07 × 1.5 = ₹6,300.

Compound interest formula

Compound interest adds each period's interest to the balance, so the next period's interest is calculated on a larger amount. That is the 'interest on interest' effect.

It is the same idea as a snowball. Each period adds a layer, and the next layer is cut from a bigger ball.

The only new idea compared with simple interest is m, the number of times per year that interest is added. The higher the m, the more often interest starts earning interest.

To apply it, work through these steps:

1. 1Write the rate as a decimal: 8% becomes 0.08.
2. 2Divide it by the number of compounding periods a year. For annual compounding, m is 1, so it stays 0.08.
3. 3Add 1 and raise the result to the power m × t. Here, 1.08 raised to the 5th power is 1.469328.
4. 4Multiply by the principal: ₹1,00,000 × 1.469328 = ₹1,46,932.81.
5. 5Subtract the principal if you only want the interest.

Raising to a power is where a calculator earns its keep. Doing it by hand is possible by multiplying 1.08 by itself five times, but the chance of a slip rises with the number of years.

Whichever route you use, state the compounding frequency next to the answer. A result without it cannot be reproduced or compared.

Simple vs compound interest on the same money

After five years the gap between simple interest and annual compounding is ₹6,932.81. The extra from switching annual to monthly compounding is smaller still, ₹2,051.76. Frequency helps, but the main effect comes from compounding at all.

How the gap widens with time

Reading across the 20-year row, simple interest has added ₹1,60,000, while compounding has added ₹3,66,096, more than twice as much. The 8% was identical in both; only the treatment of earned interest changed.

Time is the most powerful input. The extra from compounding is modest at five years and grows quickly after that, because each year's interest is calculated on a larger base.

A quick check uses the rule of 72: dividing 72 by the rate in percent gives the approximate doubling time. At 8%, 72 ÷ 8 = 9 years. Exact compound doubling takes 9.0 years, while simple interest takes 12.5 years to add the principal once.

Nominal rate versus effective annual rate

A quoted 8% compounded monthly does not equal 8% a year. The effective annual rate is (1 + 0.08 ÷ 12)^12 − 1 = 8.30%. It tells you what the money really earns in a year after compounding.

Quarterly compounding at the same nominal 8% gives an effective rate of 8.24%.

Where interest calculations go wrong

• Typing 8 where the formula needs 0.08.
• Entering months as years. Six months is 0.5 years, not 6.
• Comparing a nominal rate with an effective rate as if they were the same.
• Assuming a loan uses simple interest. Many compound or charge on a reducing balance, and flat-rate quotes can be misleading.
• Ignoring charges, taxes and withdrawal rules when comparing products.

For fixed deposits, recurring deposits and SIPs, the same ideas apply with extra details. The fixed deposit and SIP return guides on this site walk through those cases.

Compounding works against you on debt. A credit-card balance or an unpaid loan interest that is capitalised grows the same way a deposit does, only in the wrong direction.

When comparing deposit offers, ask three questions: what is the nominal rate, how often does it compound, and for how long is it locked in. Two offers with the same headline rate can end up a couple of thousand rupees apart on a lakh over five years.

A projection shows what a rate would produce, not what an investment will earn. Market-linked products do not credit a fixed rate, and a falling price can reduce your balance.