Question: Question 12 (Multiple Choice Worth 1 Points)\n(Compound Interest and Geometric Sequences LC)\n\nThe equation, $A = 2,400\left(1 + \frac{0.031}{4}\right)^{4t}$, represents the amount of money earned on a compound interest savings account. What does the value $0.031$ represent?\n\nThe value $0.031$ represents the interest rate, which means the annual compounded interest rate is 3.1%.\nThe value $0.031$ represents the interest rate, which means the annual compounded interest rate is 0.31%.\nThe value $0.031$ represents the investment period, which means the investment is invested for 0.031 years.\nThe value $0.031$ represents the investment period, which means the investment is invested for 3.1 years.
1. **State the problem:** We are given the compound interest formula $$A = 2400\left(1 + \frac{0.031}{4}\right)^{4t}$$ and asked to identify what the value $0.031$ represents.\n\n2. **Recall the compound interest formula:** The general formula for compound interest is $$A = P\left(1 + \frac{r}{n}\right)^{nt}$$ where:\n- $A$ is the amount of money accumulated after $t$ years, including interest.\n- $P$ is the principal amount (initial investment).\n- $r$ is the annual interest rate (decimal).\n- $n$ is the number of times interest is compounded per year.\n- $t$ is the time the money is invested for in years.\n\n3. **Identify the parts in the given formula:** Comparing, we see:\n- $P = 2400$\n- $r = 0.031$\n- $n = 4$ (quarterly compounding)\n- $t$ is the number of years\n\n4. **Interpret $0.031$:** Since $r$ is the annual interest rate expressed as a decimal, $0.031$ means an interest rate of $3.1\%$ per year.\n\n5. **Conclusion:** The value $0.031$ represents the annual interest rate of $3.1\%$, not the investment period.\n\n**Final answer:** The value $0.031$ represents the interest rate, which means the annual compounded interest rate is $3.1\%$.