Compound Interest Formula with Worked Examples

Compound interest adds each period's interest to the balance before the next period starts, so interest earns interest. The formula and four worked examples below use four stated assumptions: the principal is positive, the nominal annual rate is positive and fixed, there are no deposits or withdrawals during the period, and the money stays invested for whole compounding periods. Real banks and lenders set their own rates, compounding frequency, fees and taxes, so check the actual terms of any product.

The compound interest formula

For a principal P at a nominal annual rate R% per annum, compounded n times a year for t years, the amount is A = P(1 + R/(100n))^nt. The compound interest is the interest part only: CI = A - P.

P

principal, the starting amount in rupees

R

nominal annual rate in percent per annum

n

compounding periods per year (1 for annual, 2 for half-yearly)

t

time in years

A

amount, the total at the end

Under the common textbook convention for half-yearly compounding, the nominal annual rate is halved and the number of periods doubles: R/2 percent per half-year over 2t periods.

Worked examples

Example 1: annual compounding over 2 years

Find the amount and compound interest on Rs 10,000 at 10% per annum for 2 years, compounded annually.

1. Year 1 interest: 10% of 10,000 = 1,000, so the amount after year 1 is 11,000.
2. Year 2 interest: 10% of 11,000 = 1,100, so the amount after year 2 is 12,100.
3. CI = A - P = 12,100 - 10,000 = 2,100.

Amount Rs 12,100; compound interest Rs 2,100.

Example 2: three years at 5%

Find the amount and compound interest on Rs 8,000 at 5% per annum for 3 years, compounded annually.

1. A = 8000 x (1.05)³.
2. (1.05)³ = 1.157625.
3. A = 8,000 x 1.157625 = 9,261.
4. CI = 9,261 - 8,000 = 1,261.

Amount Rs 9,261; compound interest Rs 1,261.

Example 3: one year, where compound equals simple

Find the compound interest on Rs 20,000 at 10% per annum for 1 year, compounded annually, and compare it with simple interest.

1. A = 20,000 x 1.10 = 22,000, so CI = 2,000.
2. Simple interest SI = (P x R x t)/100 = (20,000 x 10 x 1)/100 = 2,000.
3. With one compounding period and the same inputs they agree.

Both give Rs 2,000.

Example 4: half-yearly compounding

Find the amount on Rs 10,000 at a nominal 10% per annum for 1 year, compounded half-yearly.

1. Half-yearly rate: 10/2 = 5 percent per half-year, over 2 periods.
2. After 6 months: 10,000 x 1.05 = 10,500.
3. After 12 months: 10,500 x 1.05 = 11,025.
4. CI = 11,025 - 10,000 = 1,025.

Amount Rs 11,025; compound interest Rs 1,025. The same inputs compounded annually give 11,000, so half-yearly compounding adds Rs 25 here.

Simple interest versus compound interest

For Rs 15,000 at 10% per annum over 2 years, simple interest is (15,000 x 10 x 2)/100 = Rs 3,000, while annual compound interest is 15,000 x (1.1)² - 15,000 = Rs 3,150. The difference is Rs 150. The comparison is conditional: for the same positive principal, the same positive nominal annual rate and the same elapsed time, compound interest over 2 or more full periods is greater than simple interest, and with exactly one full period the two are equal.

Rs 10,000 at 10% p.a., 2 years, annual

Amount Rs 12,100; compound interest Rs 2,100

Rs 8,000 at 5% p.a., 3 years, annual

Amount Rs 9,261; compound interest Rs 1,261

Rs 20,000 at 10% p.a., 1 year, annual

Amount Rs 22,000; compound interest Rs 2,000

Rs 10,000 at nominal 10% p.a., 1 year, half-yearly

Amount Rs 11,025; compound interest Rs 1,025

Frequently asked questions

Is compound interest the same as simple interest?

No. Simple interest uses the original principal; compound interest the amount including earlier interest. With one compounding period and the same inputs they agree. At the same positive principal and positive per-period rate over the same elapsed time, it is greater for 2 or more full periods.

Is compound interest always more than simple interest?

For the same positive principal, the same positive nominal annual rate and the same elapsed time, it is greater over 2 or more full periods; with exactly one full period the two are equal. Real financial products set their own terms.

What changes when interest is compounded half-yearly instead of annually?

It halves the nominal annual rate and doubles the periods: nominal 10% per annum means 5% per half-year. An effective annual rate cannot be halved this way. For a positive principal at the same positive nominal annual rate over the same elapsed time, the amount exceeds annual compounding.

Does this article tell me what a real loan or deposit will pay?

No. It only shows the arithmetic of the stated formulas under stated assumptions. Banks and lenders set their own rates, compounding frequency, fees and taxes, so check the actual terms of any product.

What is the difference between amount and compound interest?

The amount A is the total at the end: principal plus all interest. The compound interest is only the interest part: CI = A - P.

Sources and scope

Formula and conventions checked against Wikipedia, Compound interest, and MathsIsFun, Compound Interest, both retrieved 15 November 2026. This article teaches arithmetic only and makes no claim about any syllabus, board, class or real financial product.

Related reading on this site: how to solve maths word problems, the Working with Fractions chapter page, and maths tuition at EZ Tuitions.