SAT-46: Compound Interest and Percent Growth

SAT-46: Compound Interest and Percent Growth

Description: Compound interest is exponential growth applied to money: each period you earn interest on the previous total, not just the original amount. The SAT gives a standard formula.

The formula

A = P(1 + r/n)^nt

• P = principal (starting money),
• r = annual rate as a decimal (5% → 0.05),
• n = times compounded per year,
• t = number of years.

(Oʻzbekcha: P — boshlangʻich pul, r — yillik foiz (oʻnli kasr), n — yiliga necha marta, t — yillar soni.)

Why "compound" beats "simple"

Simple interest grows by the same amount each year (linear). Compound interest grows on the new, larger balance each period (exponential), so it pulls ahead over time. (Oʻzbekcha: murakkab foiz har safar yangi, kattaroq summadan hisoblanadi.)

Worked Example

$1,000 at 6% per year, compounded annually, for 3 years. P = 1000, r = 0.06, n = 1, t = 3. A = 1000(1 + 0.06/1)^{1·3} = 1000(1.06)^{3} = 1000(1.191016) ≈ $1,191.02.

Worked Example (monthly)

$2,000 at 12% per year, compounded monthly, for 2 years. r/n = 0.12/12 = 0.01, and nt = 12·2 = 24. A = 2000(1.01)^{24} ≈ $2,539.47.

Tip: "compounded monthly" means n = 12; "quarterly" n = 4; "annually" n = 1. (Oʻzbekcha: oylik → n = 12; choraklik → n = 4; yillik → n = 1.)

Practice

$500 at 4% compounded annually for 2 years — find A. Show answer A = 500(1.04)^{2} = 500(1.0816) = $540.80.

Key words — Kalit soʻzlar

• Compound interest — murakkab foiz
• Simple interest — oddiy foiz
• Principal — boshlangʻich summa (asosiy pul)
• Rate — foiz stavkasi
• Annually — yillik
• Monthly — oylik
• Quarterly — choraklik
• Balance — qoldiq (hisobdagi pul)
• Period — davr

Summary

• Compound interest: A = P(1 + r/n)^nt.
• Convert the percent to a decimal; n = compounds per year; t = years.
• Monthly n = 12, quarterly n = 4, annually n = 1.