Question

a principal of $3800 is invested at 7% 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.

For this problem:

• $P = 3800$
• $r = 7\% = 0.07$
• $n = 1$ (compounded annually)
• $t = 8$

Step2: Substitute values into formula

Substitute the values into the formula:
$A = 3800(1 + \frac{0.07}{1})^{1\times8}$
Simplify the expression inside the parentheses:
$1 + 0.07 = 1.07$
So the formula becomes:
$A = 3800\times(1.07)^{8}$

Step3: Calculate $(1.07)^8$

First, calculate $(1.07)^8$. Using a calculator, $(1.07)^8 \approx 1.71818617$

Step4: Calculate the amount $A$

Multiply the principal by the calculated value:
$A = 3800\times1.71818617$
$A \approx 3800\times1.71818617 \approx 6529.107446$

Step5: Round to nearest dollar

Round $6529.107446$ to the nearest dollar, which is $6529$

Answer:

$\$6529$