Question

a principal of $1500 is invested at 5.5% interest, compounded annually. how much will the investment be worth after 8 years? use the calculator provided and round your answer to the nearest dollar.

Explanation:

Step1: Recall compound interest formula

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where:

• $A$ is the amount of money accumulated after $n$ years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times that interest is compounded per year.
• $t$ is the time the money is invested for in years.

Here, $P = 1500$, $r = 5.5\% = 0.055$, $n = 1$ (compounded annually), and $t = 8$.

Step2: Substitute values into the formula

Substitute the values into the formula: $A = 1500(1 + \frac{0.055}{1})^{1\times8}$

Simplify the expression inside the parentheses: $1 + 0.055 = 1.055$

Then, calculate the exponent: $1\times8 = 8$

So, $A = 1500\times(1.055)^{8}$

Step3: Calculate $(1.055)^{8}$

Using a calculator, $(1.055)^{8} \approx 1.503664$

Step4: Calculate $A$

Multiply the principal by the calculated value: $A = 1500\times1.503664 \approx 2255.496$

Step5: Round to the nearest dollar

Rounding $2255.496$ to the nearest dollar gives $2255$.

Answer:

The investment will be worth $\$2255$ after 8 years.