Interest that builds on the principal and the interest already gained is called:

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

Answer: (D)

Verified step by step guidance

1. Understand the concept of compound interest: Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. It allows the interest to 'compound' over time.
2. Compare compound interest with other types of interest: Nominal interest refers to the stated interest rate without considering compounding. Discounted interest is typically used in financial instruments where interest is deducted upfront. Simple interest is calculated only on the principal amount, not on accumulated interest.
3. Recognize the key feature of compound interest: The defining characteristic of compound interest is that it builds on both the principal and the interest already earned, leading to exponential growth over time.
4. Apply the formula for compound interest if needed: The formula is \( A = P(1 + r)^n \), where \( A \) is the future value, \( P \) is the principal, \( r \) is the interest rate per period, and \( n \) is the number of periods.
5. Conclude that the correct answer to the problem is compound interest, as it matches the description provided in the question.