Compound interest

Learning Objectives Define compound interest and differentiate it from simple interest. Identify the variables (P, r, n, t) in the compound interest formula from a word problem. Calculate the future value (A) of an investment using the compound interest formula. Calculate the total interest earned over a specific period. Solve problems where the compounding period is varied (e.g., annually, semi-annually, quarterly). Apply the compound interest formula to solve real-world financial problems. Ever wonder how a small savings account can grow into a large sum of money all by itself? 💰 It's not magic, it's the power of compound interest! In this lesson, you'll learn about the powerful concept of 'interest earning interest'. We will break down the formu...

TermDefinitionExample Principal (P)The initial amount of money invested or borrowed.You deposit $1,000 into a new savings account. The principal (P) is $1,000. Interest Rate (r)The percentage of the principal earned or charged per year. In the formula, it must be expressed as a decimal.An account offers a 5% annual interest rate. For calculations, you use r = 0.05. Compounding PeriodThe frequency at which interest is calculated and added to the principal within one year.Annually (n=1), Semi-annually (n=2), Quarterly (n=4), Monthly (n=12). Time (t)The total number of years the money is invested or borrowed for.You plan to leave your money in an account for 10 years, so t = 10. Future Value (A)The total amount of money in an account after a certain period, including the principal and all th...

Compound Interest Formula A = P(1 + r/n)^(nt) This is the primary formula used to calculate the future value (A) of an investment. 'P' is the principal, 'r' is the annual interest rate as a decimal, 'n' is the number of compounding periods per year, and 't' is the time in years. Total Interest Earned Formula I = A - P To find only the amount of interest earned, subtract the initial principal (P) from the calculated future value (A).