Final answer:
The amount to which $500 will grow can be calculated using the compound interest formula under each given condition. The observed pattern of future values increasing as the compounding period shortens is due to the effect of compounding more frequently.
Step-by-step explanation:
To find the amount to which $500 will grow under each of these conditions:
- a. 12% compounded annually for 5 years: $500 * (1 + 0.12)^5 = $500 * 1.7623 = $881.15
- b. 12% compounded semiannually for 5 years: $500 * (1 + 0.06)^10 = $500 * 1.7908 = $895.40
- c. 12% compounded quarterly for 5 years: $500 * (1 + 0.03)^20 = $500 * 1.8061 = $903.05
- d. 12% compounded monthly for 5 years: $500 * (1 + 0.01)^60 = $500 * 1.7959 = $897.95
- e. 12% compounded daily for 5 years: $500 * (1 + 0.0004)^1825 = $500 * 1.799 = $899.50
f. The observed pattern of future values (FV) increasing as the compounding period shortens is due to the effect of compounding more frequently. When interest is compounded more frequently, the interest is added more often, resulting in a higher future value.