Question

sofia has $7,306 in an account. the interest rate is 8% compounded annually. to the nearest cent, how much will she have in 2 years? $

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, $P = 7306$, $r = 0.08$ (since 8% = 0.08), $n = 1$ (compounded annually), and $t = 2$.

Step2: Substitute values into the formula

Substitute the given values into the formula:
$A = 7306(1 + \frac{0.08}{1})^{1\times2}$

Step3: Simplify the expression

First, simplify the exponent and the term inside the parentheses:
$1 + \frac{0.08}{1} = 1.08$
The exponent $1\times2 = 2$, so we have $A = 7306(1.08)^2$

Step4: Calculate $(1.08)^2$

$(1.08)^2 = 1.08\times1.08 = 1.1664$

Step5: Multiply by the principal

$A = 7306\times1.1664$
Calculate the product: $7306\times1.1664 = 7306\times1 + 7306\times0.1664 = 7306 + 1215.7184 = 8521.7184$

Step6: Round to the nearest cent

Since we're dealing with money, we round to the nearest cent (two decimal places). $8521.7184$ rounded to the nearest cent is $8521.72$.

Answer:

$\$8521.72$