Find the true effective annual rate for a nominal rate compounded at a given frequency.
The stated rate is divided by how often it compounds, then compounded that many times in a year, to give one true yearly percentage.
EAR: (1 + r/n)ⁿ − 1
The effective interest rate calculator converts a nominal annual rate into the rate you actually earn or pay once compounding is included. You enter the quoted rate and how many times a year interest is compounded, and it returns the effective annual rate, often shortened to EAR or called the annual equivalent rate.
Indian financial products quote rates on different compounding bases. Bank fixed deposits commonly compound quarterly, some deposits compound half-yearly, loan interest is usually computed monthly, and credit card interest is quoted monthly. Two products both showing 10.5% can therefore deliver different amounts at the end of a year. The effective rate puts them on one footing: it is the single once-a-year rate that gives the same result.
It is the right number to use when comparing a deposit with a bond, or a loan with another loan.
1. Write the nominal annual rate as a decimal, i = rate ÷ 100.
2. Note the number of compounding periods per year n: 1 yearly, 2 half-yearly, 4 quarterly, 12 monthly, 365 daily.
3. Find the rate per period: i ÷ n.
4. Grow ₹1 for one year: (1 + i ÷ n)ⁿ.
5. Subtract 1 and multiply by 100: EAR = ((1 + i ÷ n)ⁿ − 1) × 100.
6. Compare products by their EAR, not by their nominal rate.
With quarterly compounding at 10.5%, you earn 2.625% after three months. That interest is added to your balance, so the next quarter's 2.625% is earned on a slightly larger amount. Over four quarters these small additions build up, and ₹1 grows to (1.02625)⁴ rather than 1.105. The extra is interest on interest. The more often interest is added, the earlier each piece starts earning, so the effective rate rises with the compounding frequency, though by smaller and smaller amounts.
As n grows without limit, (1 + i ÷ n)ⁿ approaches eⁱ, where e ≈ 2.71828. So even compounding every instant cannot push the effective rate above eⁱ − 1. At 12% nominal, yearly gives 12%, quarterly about 12.55%, monthly about 12.68%, daily about 12.75%, and the continuous limit is about 12.75% too. Moving from yearly to quarterly matters much more than moving from monthly to daily. This is why the daily option in the calculator is very close to the monthly one.
The nominal rate is the headline figure. The EAR adds the effect of compounding. On loans, lenders sometimes quote an APR, which aims to include fees as well; definitions vary, so read the fine print. A related confusion is the monthly rate on credit cards: 3.5% a month is 42% nominal but over 50% effective. When a product is quoted without its compounding basis, ask for it, because the effective rate cannot be worked out without knowing n.
Shalini is looking at a five-year bank deposit paying 10.5% a year, compounded quarterly, and wants to compare it with a bond that pays interest once a year.
Answer: Effective annual rate 10.92%
Comparing two nominal rates with different compounding frequencies as if they were equal.
Using the EAR where a formula expects the nominal rate, such as the monthly rate in an EMI.
Assuming daily compounding is dramatically better than monthly; the difference is small.
Ignoring that tax on interest reduces what you actually keep, whatever the EAR.
Comparing fixed deposits that compound quarterly with bonds that pay yearly.
Finding the true annual cost of a credit card or app loan quoted per month.
Checking the yield on a recurring or cumulative deposit.
Teaching compounding in commerce and finance courses.
Why does the effective rate matter?
It is the only fair way to compare two products that compound at different times. A 12% rate compounded every month is actually worth more than a 12% rate compounded once a year.