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Multiple Choice
Which of the following best describes the difference between simple interest and compound interest?
A
Simple interest is calculated on the principal and accumulated interest, while compound interest is calculated only on the principal.
B
Both simple and compound interest are calculated only on the accumulated interest.
C
Simple interest and compound interest always result in the same total interest over time.
D
Simple interest is calculated only on the principal, while compound interest is calculated on the principal plus any accumulated interest.
Verified step by step guidance
1
Understand the key concepts: Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any accumulated interest from previous periods.
Break down the formula for simple interest: \( SI = P \times r \times t \), where \( P \) is the principal, \( r \) is the annual interest rate, and \( t \) is the time in years.
Break down the formula for compound interest: \( CI = P \times (1 + r)^t - P \), where \( P \) is the principal, \( r \) is the annual interest rate, and \( t \) is the time in years. Note that compound interest includes the effect of interest on interest.
Compare the two methods: Simple interest grows linearly over time because it is based only on the principal, while compound interest grows exponentially because it includes interest on accumulated interest.
Conclude that the correct answer is: 'Simple interest is calculated only on the principal, while compound interest is calculated on the principal plus any accumulated interest.' This distinction highlights the fundamental difference between the two types of interest calculations.