Final answer:
Simple and compound interest formulas are used to calculate interest over time but differ in their approach. Simple interest is calculated only on the principal amount, while compound interest includes the effect of compounding, leading to a higher total return over time.
Step-by-step explanation:
Similarities and Differences Between Simple Interest and Compound Interest:
Simple interest and compound interest formulas both calculate the amount of interest earned on an investment over time, but they compute it differently. The simple interest formula is I = PRT, where I stands for interest, P represents the principal amount, R is the rate of interest per period, and T indicates the time the money is invested for. Simple interest is only calculated on the principal amount.
The compound interest formula has the same components but includes the compounding effect. The compound interest formula is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
To see how they operate differently, let's consider a $100 deposit at a simple interest rate of 5% held for one year, which would be: $100 x 0.05 x 1 = $5 in interest. For compound interest, if the interest is compounded annually, the calculation would be $100 x (1 + 0.05/1)^(1*1) = $105. Interest is added to the principal for the next period's interest calculation in compound interest, resulting in a higher total return over time compared to simple interest.