--- title: Compound Interest - Formula, Calculation & Examples description: Compound interest adds interest on earlier interest. This chapter shows the formula and how the compounding period changes the result. url: https://astra-ai.co/videos/financial-mathematics/compound-interest/ locale: en type: video-chapter keywords: - compound interest - interest rate - compounding - future value published: 2026-10-01T09:52:03.372Z updated: 2026-10-04T21:58:54.146Z alternates: bg: https://astra-ai.co/bg/videos/finansova-matematika/slozhna-lihva/ br: https://astra-ai.co/br/videos/matematica-financeira/capitulo-matematica-023/ cs: https://astra-ai.co/cs/videos/financni-matematika/slozene-uroceni/ da: https://astra-ai.co/da/videos/finansiel-matematik/rentes-rente/ de: https://astra-ai.co/de/videos/finanzmathematik/zinseszinsrechnung/ el: https://astra-ai.co/el/videos/oikonomika-mathimatika/anatokismos/ en: https://astra-ai.co/videos/financial-mathematics/compound-interest/ en-IN: https://astra-ai.co/en-IN/videos/financial-mathematics/chapter-e53fd0cb/ en-PH: https://astra-ai.co/en-PH/videos/financial-mathematics/chapter-e53fd0cb/ es: https://astra-ai.co/es/videos/matematica-financiera/interes-compuesto/ es-AR: https://astra-ai.co/es-AR/videos/matematica-financiera/capitulo-18/ es-CL: https://astra-ai.co/es-CL/videos/matematica-financiera/capitulo-18/ es-PE: https://astra-ai.co/es-PE/videos/matematica-financiera/capitulo-video-e53fd0cb/ et: https://astra-ai.co/et/videos/finantsmatemaatika/liitintress/ fi: https://astra-ai.co/fi/videos/talousmatematiikka/korkoa-korolle/ fr: https://astra-ai.co/fr/videos/mathematiques-financieres/interets-composes/ hr: https://astra-ai.co/hr/videos/financijska-matematika/slozene-kamate/ hu: https://astra-ai.co/hu/videos/penzugyi-matematika/kamatos-kamat/ id: https://astra-ai.co/id/videos/matematika-keuangan/bunga-majemuk/ it: https://astra-ai.co/it/videos/matematica-finanziaria/interesse-composto/ ja: https://astra-ai.co/ja/videos/financial-mathematics-ja/ja-chapter-18/ km: https://astra-ai.co/km/videos/financial-mathematics/chapter-e53fd0cb/ ko: https://astra-ai.co/ko/videos/financial-mathematics-ko/18/ lo: https://astra-ai.co/lo/videos/lo-e48299f7/lo-e53fd0cb/ lt: https://astra-ai.co/lt/videos/finansine-matematika/sudetingos-palukanos/ lv: https://astra-ai.co/lv/videos/finansu-matematika/saliktie-procenti/ ms: https://astra-ai.co/ms/videos/matematik-kewangan/bab-23-matematik-asas/ ms-BN: https://astra-ai.co/ms-BN/videos/matematik-kewangan/bab-matematik-18/ mx: https://astra-ai.co/mx/videos/matematica-financiera/capitulo-18/ my: https://astra-ai.co/my/videos/my-e48299f7/my-e53fd0cb/ nl: https://astra-ai.co/nl/videos/financiele-wiskunde/samengestelde-rente/ no: https://astra-ai.co/no/videos/finansiell-matematikk/rentes-rente/ pl: https://astra-ai.co/pl/videos/matematyka-finansowa/odsetki-zlozone/ pt: https://astra-ai.co/pt/videos/matematica-financeira/juros-compostos/ pt-TL: https://astra-ai.co/pt-TL/videos/matematica-financeira/capitulo-de-video-018/ ro: https://astra-ai.co/ro/videos/matematica-financiara/dobanda-compusa/ sk: https://astra-ai.co/sk/videos/financna-matematika/kapitola-018/ sl: https://astra-ai.co/sl/videos/financna-matematika/obrestne-obresti/ sr: https://astra-ai.co/sr/videos/finansijska-matematika/poglavlje-018/ sv: https://astra-ai.co/sv/videos/finansiell-matematik/ranta-pa-ranta/ th: https://astra-ai.co/th/videos/khanitsat-kan-ngoen/bot-23-dokbia-thop-ton/ tr: https://astra-ai.co/tr/videos/finansal-matematik/bolum-018/ uk: https://astra-ai.co/uk/videos/uk-topic-16/uk-chapter-23/ vi: https://astra-ai.co/vi/videos/vi-topic-16/vi-chapter-23/ zh-HK: https://astra-ai.co/zh-HK/videos/shuxue-kecheng-016/shuxue-zhang-023/ zh-TW: https://astra-ai.co/zh-TW/videos/financial-mathematics/chapter-e53fd0cb/ --- # Compound Interest > Compound interest adds interest on interest already earned. This chapter covers the formula and how the compounding period changes the result. ## INTRODUCTION TO COMPOUND INTEREST Compound interest is a method where interest is added not only to the initial principal but also to the accumulated interest from previous periods. This process, also known as **capitalization** of interest, means that in each compounding period, the new basis for calculating interest becomes the sum of the principal and the previously earned interest. Because of this, the value of an investment does not increase linearly but exponentially. ## BASIC FORMULA Let: - **P** be the initial **principal** (the initial amount of money), - **r** be the annual **interest rate** (in decimal form), - **n** be the **number of times that interest is compounded per year**, - **t** be the **time the money is invested or borrowed for, in years**, - **A** be the **future value** of the investment/loan after 't' years, then the formula is: **A = P \* (1 + r/n)^(n\*t)** If interest is compounded once per year (annually), then n = 1, and the formula simplifies to: **A = P \* (1 + r)^t** ## CALCULATION OF INTEREST EARNED The amount of interest (I) that the investment has earned is: **I = A – P** ## CALCULATION EXAMPLE (ANNUAL COMPOUNDING) Let's invest €1,000 at a 5% annual interest rate, with annual compounding, for a period of 3 years: - P = 1000 - r = 0.05 (5%) - n = 1 (compounded annually) - t = 3 years A = 1000 \* (1 + 0.05/1)^(1\*3) = 1000 \* (1.05)³ = 1000 \* 1.157625 = €1157.63 I = 1157.63 – 1000 = €157.63 ## EXAMPLE WITH MORE FREQUENT COMPOUNDING (QUARTERLY) If interest is compounded quarterly (n = 4): - P = €1,000 - r = 0.05 - n = 4 - t = 3 years A = 1000 \* (1 + 0.05/4)^(4\*3) = 1000 \* (1 + 0.0125)¹² = 1000 \* (1.0125)¹² (1.0125)¹² ≈ 1.1607545 A ≈ 1000 \* 1.1607545 ≈ €1160.75 With a higher frequency of compounding, the final amount is also slightly higher. ## FINAL NOTE ON GROWTH Due to the compounding effect of interest capitalization, the value of an investment increases exponentially over time. This means that a longer period and more frequent compounding significantly increase the total return. This very principle of compound interest is the foundation of long-term saving and investing. ## CONCLUSION Compound interest allows interest itself to earn interest, leading to accelerated growth of an investment. This principle is key in financial mathematics, as we encounter it in savings, loans, and long-term investments.