Question

a principal of $2400 is invested at 3.5% interest, compounded annually. how much will the investment be worth after 7 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.

In this problem, $P = 2400$, $r = 3.5\% = 0.035$, $n = 1$ (compounded annually), and $t = 7$.

Step2: Substitute values into the formula

Substitute the given values into the formula:
$A = 2400(1 + \frac{0.035}{1})^{1 \times 7}$
Simplify the expression inside the parentheses:
$1 + 0.035 = 1.035$
So the formula becomes:
$A = 2400(1.035)^{7}$

Step3: Calculate the value of $(1.035)^7$ and then multiply by 2400

First, calculate $(1.035)^7$. Using a calculator, $(1.035)^7 \approx 1.272279$ (you can calculate this by raising 1.035 to the power of 7).

Then multiply this by 2400:
$A = 2400 \times 1.272279 \approx 3053.47$

Step4: Round to the nearest dollar

Rounding 3053.47 to the nearest dollar gives 3053.

Answer:

3053