Question

find the value of the investment after the specified time period. round to the nearest cent. a $2500 investment compounded annually at a 5.5% interest rate for 8 years enter the correct value in the box. show hints

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, since it's compounded annually, $n = 1$, $P=\$2500$, $r = 5.5\%=0.055$, and $t = 8$ years.

Step2: Substitute values into the formula

Substitute $P = 2500$, $r=0.055$, $n = 1$, and $t = 8$ into the formula:
$A=2500(1+\frac{0.055}{1})^{1\times8}$
Simplify the expression inside the parentheses first: $1+\frac{0.055}{1}=1.055$
Then we have $A = 2500\times(1.055)^{8}$

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

Using a calculator, $(1.055)^{8}\approx1.503668$

Step4: Calculate $A$

Multiply the principal by the result from Step 3:
$A=2500\times1.503668 = 3759.17$ (rounded to the nearest cent)

Answer:

$\$3759.17$