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 $I = P \cdot r \cdot t$ (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: This is false; simple interest only applies to the original principal.
3. Compound interest earns more money than simple interest at the same rate for the same amount of time: For time periods longer than 1 year, compound interest (earned on principal + accumulated interest) will exceed simple interest. This is true.
4. Simple interest earns more money than compound interest at the same rate for the same amount of time: This is false, as compound interest outpaces simple interest over time.
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: This is false; simple interest generates a fixed annual interest amount, while compound interest's annual earnings increase.
7. Only simple interest uses time in its formula: This is false; both simple and compound interest formulas include a time variable.
8. Compound interest is earned on principal and interest: This is the core definition of compound interest (interest is compounded on the growing balance). 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.