If you invest $1,000 at a 6% annual interest rate, how much will it be worth in 5 years with annual compounding?a.$1,338.22b.$1,060c.$1,300d.$1,500

1. Break Down the Problem

We need to find the future value of an investment given the initial principal, interest rate, time period, and compounding frequency.

2. Relevant Concepts

The formula for calculating the future value $FV$ of an investment with compound interest is given by: $FV = P \left(1 + \frac{r}{n}\right)^{nt}$ where:

• $P$ is the principal amount (the initial investment),
• $r$ is the annual interest rate (as a decimal),
• $n$ is the number of times that interest is compounded per year,
• $t$ is the number of years the money is invested or borrowed.

Given:

• $P = 1000$
• $r = 6\% = 0.06$
• $n = 1$ (compounding annually)
• $t = 5$

3. Analysis and Detail

Now, substitute the values into the formula: $FV = 1000 \left(1 + \frac{0.06}{1}\right)^{1 \times 5}$ $= 1000 \left(1 + 0.06\right)^{5}$ $= 1000 \left(1.06\right)^{5}$

Now calculate $(1.06)^5$: $(1.06)^5 \approx 1.338225$ Thus, $FV \approx 1000 \times 1.338225 \approx 1338.225$

4. Verify and Summarize

After performing the calculations: Future Value $FV \approx 1338.22$.

Final Answer

The investment will be worth approximately $1,338.22**, so the correct answer is **a.$1,338.22.