Question

which descriptions about simple interest and yearly compounded interest are true? select four options. only compound interest has an exponent in its formula. simple interest is earned on principal and interest. compound interest earns more money than simple interest at the same rate for the same amount of time. simple interest earns more money than compound interest at the same rate for the same amount of time. simple interest is only earned on the original principal investment. only compound interest earns the same interest amount every year. only simple interest uses time in its formula. compound interest is earned on principal and interest.

Explanation:

1. Only compound interest has an exponent in its formula: The simple interest formula is $I = P \times r \times t$ (no exponent), while the yearly compound interest formula is $A = P(1+r)^t$ (has an exponent for time $t$). This is true.
2. Simple interest is earned on principal and interest: Simple interest only applies to the original principal, not accumulated interest. This is false.
3. Compound interest earns more money than simple interest at the same rate for the same amount of time: Compound interest earns interest on prior interest, so it will exceed simple interest (for time > 1 year, positive rate, non-zero principal). This is true.
4. Simple interest earns more money than compound interest at the same rate for the same amount of time: This directly contradicts the logic above. This is false.
5. Simple interest is only earned on the original principal investment: This is the core definition of simple interest. This is true.
6. Only compound interest earns the same interest amount every year: Simple interest generates a fixed annual interest amount ($P \times r$), while compound interest's annual interest grows each year. This is false.
7. Only simple interest uses time in its formula: Both simple and compound interest formulas include time $t$ as a variable. This is false.
8. Compound interest is earned on principal and interest: This is the core definition of compound interest (earning interest on interest). This is true.

Answer:

• Only compound interest has an exponent in its formula.
• Compound interest earns more money than simple interest at the same rate for the same amount of time.
• Simple interest is only earned on the original principal investment.
• Compound interest is earned on principal and interest.