Question

rob has $7,869 in an account that earns 13% interest compounded annually. to the nearest cent, how much will he have in 5 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, since it's compounded annually, $n = 1$, $P = 7869$, $r = 0.13$ (because 13% = 0.13), and $t = 5$.

Step2: Substitute the values into the formula

Substitute $P = 7869$, $r = 0.13$, $n = 1$, and $t = 5$ into the formula:
$A = 7869(1 + \frac{0.13}{1})^{1\times5}$

Step3: Simplify the expression

First, simplify the exponent and the fraction inside the parentheses:
$\frac{0.13}{1}=0.13$, and $1 + 0.13 = 1.13$. The exponent $1\times5 = 5$. So the formula becomes:
$A = 7869\times(1.13)^{5}$

Now, calculate $(1.13)^{5}$. Let's compute that:
$(1.13)^{5}=1.13\times1.13\times1.13\times1.13\times1.13$
$1.13\times1.13 = 1.2769$
$1.2769\times1.13 = 1.442897$
$1.442897\times1.13 = 1.63047361$
$1.63047361\times1.13 = 1.8424351793$

Then, multiply this by the principal:
$A = 7869\times1.8424351793$

Step4: Calculate the final amount

$7869\times1.8424351793 \approx 14498.12$ (rounded to the nearest cent)

Answer:

$\$14498.12$