Which type of interest earns a bigger rate of return on a deposit over time, assuming the same nominal rate and compounding period?

• A. Compound interest
• B. Simple interest
• C. Nominal interest
• D. Discounted interest

Answer: (A)

Verified step by step guidance

1. Understand the concept of simple interest: Simple interest is calculated only on the principal amount of a deposit, without considering any interest earned in previous periods. The formula for simple interest is \( I = P \cdot r \cdot t \), where \( P \) is the principal, \( r \) is the annual interest rate, and \( t \) is the time in years.
2. Understand the concept of compound interest: Compound interest is calculated on the principal amount and also on the accumulated interest from previous periods. The formula for compound interest is \( A = P \cdot (1 + r)^t \), where \( A \) is the total amount after interest, \( P \) is the principal, \( r \) is the annual interest rate, and \( t \) is the time in years.
3. Compare the two types of interest: Over time, compound interest earns a bigger rate of return because it takes into account the interest earned in previous periods, which is added to the principal for future calculations. Simple interest, on the other hand, does not compound and only applies to the original principal.
4. Consider the nominal interest rate: The nominal interest rate is the stated annual rate without adjustments for compounding. It does not directly indicate the rate of return over time unless the compounding frequency is specified.
5. Understand discounted interest: Discounted interest refers to interest that is deducted upfront from the principal amount, often used in loans or bonds. It does not earn a bigger rate of return compared to compound interest over time.