Compound interest: word problems

Learning Objectives Identify the principal, interest rate, compounding frequency, and time from a word problem. Set up and solve compound interest problems to find the future value (A). Algebraically manipulate the compound interest formula to solve for the principal (P). Apply logarithms to solve for the time (t) required to reach a specific financial goal. Differentiate between and apply the formulas for periodic and continuous compounding. Analyze and compare different investment scenarios to determine the better option. If you invested $1,000 today, how long would it take to double your money without adding another cent? 📈 This tutorial will unlock the power of exponential functions to solve real-world financial questions. You will learn to model investment growth and...

TermDefinitionExample Principal (P)The initial amount of money invested or borrowed.If you deposit $5,000 into a new savings account, the principal (P) is $5,000. Interest Rate (r)The percentage of the principal earned or paid as interest over a specific time period, always expressed as a decimal in calculations.An annual interest rate of 4% means r = 0.04. Compounding PeriodThe interval of time at which accumulated interest is added to the principal, so that future interest is earned on the new, larger amount.If interest is compounded 'quarterly', it is calculated and added to the principal 4 times per year. Number of Compounding Periods per Year (n)The frequency with which interest is compounded in one year.Annually: n=1; Semi-annually: n=2; Quarterly: n=4; Monthly: n=12; Dail...

Compound Interest Formula A = P(1 + \frac{r}{n})^{nt} Use this formula when interest is compounded a specific number of times per year (n). A is the future value, 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. Continuous Compounding Formula A = Pe^{rt} Use this formula for the theoretical case where interest is compounded infinitely many times per year. 'e' is Euler's number, an irrational constant approximately equal to 2.71828. Formula to Solve for Time (t) t = \frac{\ln(\frac{A}{P})}{n \cdot \ln(1 + \frac{r}{n})} This is a rearranged version of the standard compound interest formula, derived using natural logarithms (ln). It is used to calculate the time it...